GEMath Flashcards

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Questions and Answers

What is the result of the operation $A ∪ (B ∩ C)$?

Elements in B only

Elements in B or C but not A

Elements in A only

Elements in A plus elements that are in both B and C (correct)

The intersection of three sets, $A ∩ B ∩ C$, contains only the elements that are present in all three sets.

True

What is the symbol for the empty set?

∅

The function $f: A \rightarrow B$ indicates that for each element in set A, there is a corresponding element in set ______.

B Signup and view all the answers

Match the following operations with their results:

A ∩ B = Elements common to both A and B A ∪ B = All elements in A or B or both A × B = All ordered pairs (a, b) where a ∈ A and b ∈ B A - B = Elements in A that are not in B Signup and view all the answers

What is a defining characteristic of a function mapping from set A to set B?

Each element of A has a single mapping in B Signup and view all the answers

In a function, an element of set B can be associated with multiple elements from set A.

True Signup and view all the answers

What is the graphical representation of a function often referred to in mathematics?

Graph or Plot Signup and view all the answers

In a function 𝑓: 𝐴 → 𝐵, if 𝑓(𝑎) = 𝑏, then the element 𝑏 is the ______ of 𝑎.

image Signup and view all the answers

Match the elements with their descriptions.

Set A = Domain of the function Set B = Codomain of the function Mapping = Relationship between elements of A and B Function = Specific type of relation with unique outputs for each input Signup and view all the answers

Which of the following is an example of an infinite sequence?

1, 1/2, 1/3, 1/4, 1/5, … Signup and view all the answers

A finite sequence must have a last number.

True Signup and view all the answers

What is the common ratio in the geometric sequence 1, 2, 4, 8, 16, 32?

2 Signup and view all the answers

The common difference in the arithmetic sequence 11, 7, 3, -1, -5, -9 is _____ .

4 Signup and view all the answers

Match the type of sequence with its characteristic:

Geometric Sequence = Has a common ratio Arithmetic Sequence = Has a common difference Finite Sequence = Has a last number Infinite Sequence = Continues indefinitely Signup and view all the answers

Which of the following sequences is an example of an arithmetic progression?

2, 4, 6, 8, 10 Signup and view all the answers

In an infinite sequence, the terms can be counted.

False Signup and view all the answers

What is the last term of the finite sequence 2, 4, 6, 8, 12, 14?

14 Signup and view all the answers

Which of the following sets are subsets of U = {1, 3, 5, 7, 9, 11, 13}?

{1, 9, 5, 13} Signup and view all the answers

The set of integers can be a universal set for the set of natural numbers.

True Signup and view all the answers

What is the power set of A = {1, 2, 3}?

{{1,2,3}, {1,2}, {1,3}, {2,3}, {1}, {2}, {3}, ⊘} Signup and view all the answers

The number of subsets of a set containing n elements is ______.

2^n Signup and view all the answers

Match the following sets to their characteristics:

The set of even natural numbers = A subset of the natural numbers The set of negative numbers = Includes only integers less than zero The set of odd natural numbers = A distinct subset of the natural numbers The set of natural numbers = Includes all positive whole numbers Signup and view all the answers

In a function represented as $f: A ightarrow B$, what is true about the elements of set A?

Each element of A has a single mapping in B Signup and view all the answers

In a function, an element of set B may be mapped to by multiple elements in set A.

True Signup and view all the answers

What is the term used to describe the graphical representation of a function?

Graph Signup and view all the answers

In the function notation $f: A ightarrow B$, if $f(a) = b$, then $b$ is the ______ of $a$.

image Signup and view all the answers

Match the following terms with their definitions:

Function = A relationship between two sets where each element of the first set is associated with one element of the second set Mapping = The process of associating elements from one set to another Set A = The domain of the function Set B = The codomain of the function Signup and view all the answers

What term describes the set of all possible outputs for a function?

Range Signup and view all the answers

The preimage of an element in the co-domain is referred to as its image.

False Signup and view all the answers

What is the notation used to denote the domain of a function?

dom(f) Signup and view all the answers

If $f: A ightarrow B$, then for an element $a$ in the domain, its corresponding output is $f(a) = ______$.

b Signup and view all the answers

Match the following function components to their definitions:

A = Domain of the function B = Co-domain of the function b = Image of an element a = Preimage of an image Signup and view all the answers

What operation combines two functions by applying one function to the output of another?

Composition Signup and view all the answers

For two functions, $f$ and $g$, it holds that $f ullet g = g ullet f$.

False Signup and view all the answers

What is the result of the operation $(f + g)(x)$ defined for functions $f$ and $g$?

f(x) + g(x) Signup and view all the answers

What is the value of $loor{-3.2}$?

-4 Signup and view all the answers

What is the output of $loor{1.5}$?

1 Signup and view all the answers

$loor{x} = x$ if and only if $x$ is an integer.

True Signup and view all the answers

What is the value of $loor{-1.4}$?

-2 Signup and view all the answers

What is the value of $loor{-3}$?

-3 Signup and view all the answers

The ceiling function $ig floor x ig floor$ for $x = -1.4$ is equal to ______.

-1 Signup and view all the answers

Match the following values with their respective functions (floor and ceiling):

$loor{2}$ = 2 $ig floor 2 ig floor$ = 2 $loor{-2.3}$ = -3 $ig floor -2.3 ig floor$ = -2 Signup and view all the answers

What is the output of the ceiling function $ig floor 1.5 ig floor$?

2 Signup and view all the answers

What type of correspondence is described by both one-to-one and onto functions?

Bijective (both one-to-one and onto) Signup and view all the answers

The inverse of a bijective function is uniquely determined.

True Signup and view all the answers

What is the value of the floor function $lloor 2.8 floor$?

2 Signup and view all the answers

For a function 𝑓: 𝐴→𝐵, the composition of 𝑓 and its inverse is the __________ function.

identity Signup and view all the answers

Match the following function types with their definitions:

Injective = A function where each output is from exactly one input Surjective = A function that covers every element in the codomain Bijective = A function that is both injective and surjective Identity = A function that maps every input to itself Signup and view all the answers

Which of the following best describes the ceiling function?

The smallest integer greater than or equal to x Signup and view all the answers

If x is an integer, then $lloor x floor = x$.

True Signup and view all the answers

What is the result of the ceiling function $ceil -2.3 ceil$?

-2 Signup and view all the answers

How many subsets does a set containing 5 elements have?

32 Signup and view all the answers

The set of negative numbers can be considered a universal set for all sets of natural numbers.

False Signup and view all the answers

What is the correct power set for the set A = {1, 2, 3}?

{{1,2,3}, {1,2}, {1,3}, {2,3}, {1}, {2}, {3}, ⊘} Signup and view all the answers

The subset that contains only the element 9 and 5 from the universal set U = {1, 3, 5, 7, 9, 11, 13} is ______.

{5, 9} Signup and view all the answers

Match the following sets with their characteristics:

A = {0} = Not a subset of U B = {2, 4} = Not a subset of U C = {1, 9, 5, 13} = Subset of U D = {5, 11, 1} = Subset of U E = {13, 7, 9, 11, 5, 3, 1} = Subset of U F = {2, 3, 4, 5} = Not a subset of U Signup and view all the answers

What is the value of the floor function for $-3.2$?

-4 Signup and view all the answers

The ceiling function of $1.5$ is equal to 2.

True Signup and view all the answers

What is the value of the ceiling function for $-1.4$?

-1 Signup and view all the answers

The value of the floor function $loor{2}$ is ______.

2 Signup and view all the answers

Match the numerical value with the correct function output (floor or ceiling):

Floor of 1.5 = 1 Ceiling of -3.2 = -3 Floor of -1.4 = -2 Ceiling of 2 = 2 Signup and view all the answers

Which of these values represents the ceiling function output for $1.5$?

2 Signup and view all the answers

The floor function for any integer $x$ is equal to $x$.

True Signup and view all the answers

What is the value of floor function $loor{-3}$?

-3 Signup and view all the answers

What is a defining characteristic of a finite sequence?

It has a last number. Signup and view all the answers

A geometric progression has a common difference between its consecutive terms.

False Signup and view all the answers

What is the common ratio of the geometric sequence 1, 2, 4, 8, 16, 32?

2 Signup and view all the answers

In an arithmetic progression, the common difference of the sequence 11, 7, 3, -1, -5, -9 is _____ .

-4 Signup and view all the answers

Match the following types of sequences with their characteristics:

Geometric Sequence = Common ratio between terms Arithmetic Sequence = Common difference between terms Finite Sequence = Has a last term Infinite Sequence = No last term Signup and view all the answers

Which of the following is an example of an infinite sequence?

1, 1/2, 1/3, 1/4, 1/5, ... Signup and view all the answers

An arithmetic sequence can have a common ratio.

False Signup and view all the answers

What is the last term of the finite sequence 2, 4, 6, 8, 12, 14?

14 Signup and view all the answers

What represents the operation of conjunction in Boolean algebra?

∧ Signup and view all the answers

The Boolean product of two matrices uses addition and multiplication as defined in standard matrix operations.

False Signup and view all the answers

What is the common operation used to replace multiplication in the Boolean product of matrices?

AND Signup and view all the answers

The resulting matrix from the Boolean product of two matrices is defined using the operations _ and _.

∨, ∧ Signup and view all the answers

Match the following terms with their definitions:

∨ = OR operation ∧ = AND operation Zero-One Matrix = A matrix containing only 0s and 1s Determinant = A scalar value that can be computed from elements of a square matrix Signup and view all the answers

In matrix operations involving Boolean algebra, which element is exchanged to find the inverse of a 2x2 matrix?

Elements on the main diagonal Signup and view all the answers

What is the next term in the sequence 1, 6, 11, 16, ...?

21 Signup and view all the answers

The Boolean product of two matrices gives a result that could include elements other than 0 and 1.

False Signup and view all the answers

What is the result when applying the operation ∧ to two binary values both equal to 1?

1 Signup and view all the answers

The Fibonacci sequence is defined by a recurrence relation.

True Signup and view all the answers

What are the elements of the function defined by f(n) = 5n for n = (1,2,3,4,5)?

(5, 10, 15, 20, 25) Signup and view all the answers

The next term in the sequence 1, 3, 6, 10, ... is _____ .

15 Signup and view all the answers

Match the following function descriptions with their corresponding sequences:

f(n) = 5n = Finite sequence 1, 8, 27, 64 = Cubic sequence 1, 3, 5, 7 = Odd numbers 20, 17, 13 = Decreasing sequence Signup and view all the answers

What is the 20th element of the arithmetic sequence that starts with 14 and has a second element of 9?

4 Signup and view all the answers

The pair (1,5) is an ordered pair in the function defined by f(n) = 5n.

True Signup and view all the answers

What is the first term of the sequence defined by f(n) = 5n?

5 Signup and view all the answers

In the function notation $f: A ightarrow B$, if $f(a) = b$, which statement is true?

Element $b$ is the output of function $f$. Signup and view all the answers

In a function represented by $f: A ightarrow B$, each element of set B must be mapped to at least one element in set A.

False Signup and view all the answers

What is a distinctive characteristic of functions in terms of their mapping?

Each element of set A maps to exactly one element in set B. Signup and view all the answers

A graphical representation of a function can include a ______ diagram.

Venn Signup and view all the answers

Match the following terms with their descriptions:

One-to-one = A function where each element of A maps to a unique element of B Onto = A function where every element of B is mapped by some element of A Bijective = A function that is both one-to-one and onto Image = The output or result of a function on an element of its domain Signup and view all the answers

What characterizes a finite sequence?

It contains a last element. Signup and view all the answers

An infinite sequence has a last number that follows the defined pattern.

False Signup and view all the answers

What is the common difference in the arithmetic sequence 11, 7, 3, -1, -5, -9?

4 Signup and view all the answers

The ratio between consecutive terms in the geometric sequence 1, 2, 4, 8, 16, 32 is called the ______.

common ratio Signup and view all the answers

Match the following sequences with their characteristics:

Geometric Sequence = A sequence with a constant ratio between terms Arithmetic Sequence = A sequence with a constant difference between terms Finite Sequence = A sequence that ends with a specific last number Infinite Sequence = A sequence that does not end and continues indefinitely Signup and view all the answers

Which of the following is an example of a finite sequence?

5, 10, 15, 20, 25 Signup and view all the answers

An arithmetic sequence can contain both positive and negative differences between terms.

True Signup and view all the answers

What is an example of an infinite sequence?

1, 1/2, 1/3, 1/4, ... Signup and view all the answers

What is a set commonly described as?

An unordered collection of objects Signup and view all the answers

A set can be described using lowercase letters for its elements.

True Signup and view all the answers

What is the correct roster notation for the set of all even whole numbers between 0 and 10?

{2, 4, 6, 8} Signup and view all the answers

In set theory, a collection of objects or members is called a ______.

set Signup and view all the answers

Match the following set descriptions with their correct notation:

Roster method = Lists elements explicitly Set builder notation = Describes elements that satisfy a condition Interval notation = Represents a range of numbers Signup and view all the answers

Which of the following correctly represents a set of all suits in a standard deck of playing cards?

{hearts, diamonds, clubs, spades} Signup and view all the answers

Members of a set are always listed in a specific order.

False Signup and view all the answers

Give an example of a set using the roster method for the set of all fingers.

{thumb, index, middle, ring, little} Signup and view all the answers

What is the value of $loor{-1.4}$?

-2 Signup and view all the answers

$loor{x} = x$ if and only if $x$ is an integer.

True Signup and view all the answers

What is the output of the ceiling function $ig floor 1.5 ig floor$?

2 Signup and view all the answers

The value of $loor{-3.2}$ is ______.

-4 Signup and view all the answers

Match the following values with their respective functions (floor and ceiling):

$loor{-3}$ = -3 $ig floor{-1.4}ig floor$ = -1 $loor{2.8}$ = 2 $ig floor{1.5}ig floor$ = 2 Signup and view all the answers

What is the value of $ig floor 2 ig floor$?

2 Signup and view all the answers

The ceiling function of a negative decimal number always results in a negative integer.

False Signup and view all the answers

What is the value of $loor{1.5}$?

1 Signup and view all the answers

Which of the following matrices is symmetric?

A = [[1, 1], [1, 1]] Signup and view all the answers

A zero-one matrix is defined as a matrix that consists entirely of the entries 0 and 1.

True Signup and view all the answers

What is the primary characteristic of a symmetric matrix?

It is equal to its transpose. Signup and view all the answers

A matrix that is symmetric must be a ______ matrix.

square Signup and view all the answers

Match the following terms with their meanings:

Symmetric Matrix = Equal to its transpose Zero-One Matrix = Contains only 0s and 1s Power of a Matrix = Matrix multiplied by itself Transpose of a Matrix = Rows become columns Signup and view all the answers

Which of the following statements about powers of matrices is correct?

Matrix powers can only be computed for square matrices. Signup and view all the answers

What type of arithmetic do zero-one matrices use?

Boolean arithmetic Signup and view all the answers

For a matrix to be symmetric, it can be non-square.

False Signup and view all the answers

Study Notes

Sets and Venn Diagrams

Understanding of unions and intersections of sets using Venn diagrams.
For set operations:
- A ∪ B ∪ C represents the union of sets A, B, and C.
- A ∩ B ∩ C represents the intersection of sets A, B, and C.
- A ∪ (B ∩ C) combines set A with the intersection of sets B and C.

Review Statements

Evaluate statements as TRUE or FALSE based on set operations:
- Union and intersection require accurate representation of elements.
- Attention to the empty set's properties when multiplying sets.

Functions

A function ( f: A \rightarrow B ) maps each element ( x \in A ) to exactly one element ( f(x) \in B ).
Functions can have single or multiple elements from domain A mapping to elements in codomain B.

Sequences

Finite Sequence: A sequence with a specific ending (e.g., 2, 4, 6, 8, 12, 14).
Infinite Sequence: A sequence that continues indefinitely, represented with ellipsis (e.g., 1, 1/2, 1/3, ...).

Examples of Sequences

Geometric Progression: Each term after the first is generated by multiplying the previous term by a fixed number (common ratio). Example: 1, 2, 4, 8, 16, with a common ratio ( r = 2 ).
Arithmetic Progression: Each term after the first is generated by adding a fixed number (common difference). Example: 11, 7, 3, -1, -5, with a common difference of 4.

Graphical Representations

Functions can be visually represented through various methods, including:
- Venn diagrams to show set relations.
- Graphs to depict relationships between variables.
- Plots to illustrate data points in a coordinate system.

Terminology in Functions

A mathematical notation ( f(a) = b ) indicates that when element ( a ) from set A is input into function ( f ), it gives output ( b ) in set B.

Basic Concepts of a Set

Set B includes all even natural numbers (B = {x | x ∈ W, x = 2n}).

Power Set

The power set of A = {1, 2, 3} consists of all possible subsets.
P(A) = {{1, 2, 3}, {1, 2}, {1, 3}, {2, 3}, {1}, {2}, {3}, ⊘}.

Set Cardinality

Number of elements in a set is known as its cardinality.

Subset Practice

Universal set U = {1, 3, 5, 7, 9, 11, 13}.
Subsets of U identified include:
- C = {1, 9, 5, 13},
- D = {5, 11, 1},
- E = {13, 7, 9, 11, 5, 3, 1}.

Universal Set

The set of integers (C) serves as a universal set for other sets like even/odd natural numbers.

Number of Subsets

A set with 5 elements contains 32 subsets (2^5).
A set with cardinality 9 contains 512 subsets (2^9).

Functions Terminology

Domain of function f: dom(f) = A.
Co-domain of function f: B.
Image of element a in A: f(a) = b.
Preimage of b: a.
Range of f: rng(f) is all images of elements from A.

Function Visualization

Functions are visualized through diagrams like Venn diagrams or graph plots.

Function Operations

Functions f and g can be added: (f + g)(x) = f(x) + g(x).
Functions can be multiplied: (f × g)(x) = f(x) × g(x).

Function Composition

Composition of functions: (f ○ g)(a) = f(g(a)).
Order matters; generally, f ○ g ≠ g ○ f.

Inverse of a Function

For bijections f: A → B, the inverse f⁻¹ exists such that f⁻¹(f(a)) = a.

Important Functions

Floor function (⌊x⌋) returns the largest integer less than or equal to x.
Ceiling function (⌈x⌉) returns the smallest integer greater than or equal to x.

Visualization of Floor & Ceiling Functions

Real numbers round down to their floor and up to their ceiling.
If x is an integer, then ⌊x⌋ = ⌈x⌉ = x.

Example Values

⌊-3.2⌋ = -4.
⌊1.5⌋ = 1.
⌈1.5⌉ = 2.
⌈2⌉ = 2.

Sets and Power Sets

Set B consists of all even natural numbers defined by the formula B = {x | x ∈ W, x = 2n}.
The power set P(A) of A = {1, 2, 3} includes all possible subsets: {{1,2,3}, {1,2}, {1,3}, {2,3}, {1}, {2}, {3}, ∅}.

Set Cardinality and Subsets

Subset identification of universal set U = {1, 3, 5, 7, 9, 11, 13} shows valid subsets as C = {1, 9, 5, 13}, D = {5, 11, 1}, and E = {13, 7, 9, 11, 5, 3, 1}.
A universal set among given options is the set of integers (option c), which contains all other types of numbers.

Calculating Subsets

The number of subsets for a set with 5 elements is 2^5 = 32.
For a set with 9 elements, the number of subsets is 2^9 = 512.

Floor and Ceiling Functions

The floor function ⌊x⌋ returns the greatest integer less than or equal to x, while the ceiling function ⌈x⌉ returns the smallest integer greater than or equal to x.
Example of floor function: ⌊-3.2⌋ = -4, ⌊1.5⌋ = 1.
Example of ceiling function: ⌈1.5⌉ = 2, ⌈2⌉ = 2.

Sequence Definitions

Finite sequence: A sequence with a last number. Example: 2, 4, 6.
Infinite sequence: A sequence with no last number. Example: 1, 1/2, 1/3, and so on.

Types of Sequences

Geometric sequence: Each term is multiplied by a constant (common ratio). Example: 1, 2, 4, 8 (common ratio r = 2).
Arithmetic sequence: Each term is derived by adding a constant (common difference). Example: 11, 7, 3 (common difference = -4).

Recurrence Relations

Recurrence relations define the next terms in sequences based on previous terms, as seen in the Fibonacci sequence.

Exercises on Sequences

Identifying next terms from given sequences:
- 1, 6, 11, 16, … → 21.
- 1, 8, 27, 64, … → 125.
- 1, 3, 6, 10, … → 15.
- 20, 17, 13, 8, … → 2.
- 1, 3, 5, 7, 9, … → 11.

Zero-One Matrices

Operations on zero-one matrices involve using Boolean algebra; addition is replaced by OR (∨), and multiplication by AND (∧).
The matrix operations yield different results compared to standard arithmetic.

Inverse of a 2x2 Matrix

To find the inverse of a matrix A defined as: [ A = \begin{pmatrix} a & b \ c & d \end{pmatrix} ] exchange elements of the main diagonal and change the signs of the off-diagonal elements then divide by the determinant.

Chapter Overview

Covers foundational topics in Discrete Mathematics: Sets, Functions, Sequences and Summations, and Matrices.

Basic Concepts of a Set

A set is an unordered collection of unique objects, called elements or members.
Common notation: uppercase letters represent sets; lowercase letters denote elements.

Set Descriptions

Roster Method: Lists some elements of a set followed by ellipses to indicate continuation (e.g., {1, 2, ...}).
Set Builder Notation: Describes elements based on a property, e.g., {x | x > 0} for all positive numbers.
Interval Notation: Represents a range of numbers (e.g., (1, 5] includes numbers greater than 1 and up to 5).

Examples of Set Descriptions

Set of all fingers: P = {thumb, index, middle, ring, little}.
Set of even whole numbers between 0 and 10: Q = {2, 4, 6, 8}.

Functions

Functions are mappings from set A to set B, denoted as f: A → B.
Specific function values can be calculated using floor and ceiling functions.
Floor function, ⌊x⌋, returns the greatest integer less than or equal to x.
Ceiling function, ⌈x⌉, returns the smallest integer greater than or equal to x.

Graphical Representations

Functions can be displayed graphically using various formats like Venn diagrams, graphs, and plots.

Sequences

Finite Sequence: A sequence with a last number (e.g., 2, 4, 6, 8, 12, 14).
Infinite Sequence: A sequence that continues indefinitely (e.g., 1, 1/2, 1/3, ...).
Geometric Progression: A sequence where each term is obtained by multiplying the previous one by a constant (common ratio).
Arithmetic Progression: A sequence where each term differs from the preceding one by a constant (common difference).

Matrices

A matrix is an array of numbers arranged in rows and columns.
Symmetric Matrix: A square matrix is symmetric if it mirrors across its main diagonal.
Zero-One Matrix: A matrix with entries of only 0s and 1s, used in algorithms based on Boolean arithmetic.

Sample Problems

Floor function values:
- ⌊−3.2⌋ = -4
- ⌊1.5⌋ = 1
- ⌈1.5⌉ = 2
- ⌈2⌉ = 2

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Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of sets, Venn diagrams, and functions in this comprehensive quiz. You'll explore unions, intersections, functions, and sequences, evaluating statements as TRUE or FALSE. Prepare to challenge your knowledge of set operations and sequence types!

GEMath Flashcards

Choose a study mode

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Questions and Answers

What is the result of the operation $A ∪ (B ∩ C)$?

The intersection of three sets, $A ∩ B ∩ C$, contains only the elements that are present in all three sets.

What is the symbol for the empty set?

The function $f: A \rightarrow B$ indicates that for each element in set A, there is a corresponding element in set ______.

Match the following operations with their results:

What is a defining characteristic of a function mapping from set A to set B?

In a function, an element of set B can be associated with multiple elements from set A.

What is the graphical representation of a function often referred to in mathematics?

In a function 𝑓: 𝐴 → 𝐵, if 𝑓(𝑎) = 𝑏, then the element 𝑏 is the ______ of 𝑎.

Match the elements with their descriptions.

Which of the following is an example of an infinite sequence?

A finite sequence must have a last number.

What is the common ratio in the geometric sequence 1, 2, 4, 8, 16, 32?

The common difference in the arithmetic sequence 11, 7, 3, -1, -5, -9 is _____ .

Match the type of sequence with its characteristic:

Which of the following sequences is an example of an arithmetic progression?

In an infinite sequence, the terms can be counted.

What is the last term of the finite sequence 2, 4, 6, 8, 12, 14?

Which of the following sets are subsets of U = {1, 3, 5, 7, 9, 11, 13}?

The set of integers can be a universal set for the set of natural numbers.

What is the power set of A = {1, 2, 3}?

The number of subsets of a set containing n elements is ______.

Match the following sets to their characteristics:

In a function represented as $f: A ightarrow B$, what is true about the elements of set A?

In a function, an element of set B may be mapped to by multiple elements in set A.

What is the term used to describe the graphical representation of a function?

In the function notation $f: A ightarrow B$, if $f(a) = b$, then $b$ is the ______ of $a$.

Match the following terms with their definitions:

What term describes the set of all possible outputs for a function?

The preimage of an element in the co-domain is referred to as its image.

What is the notation used to denote the domain of a function?

If $f: A ightarrow B$, then for an element $a$ in the domain, its corresponding output is $f(a) = ______$.

Match the following function components to their definitions:

What operation combines two functions by applying one function to the output of another?

For two functions, $f$ and $g$, it holds that $f ullet g = g ullet f$.

What is the result of the operation $(f + g)(x)$ defined for functions $f$ and $g$?

What is the value of $ loor{-3.2}$?

What is the output of $ loor{1.5}$?

$ loor{x} = x$ if and only if $x$ is an integer.

What is the value of $ loor{-1.4}$?

What is the value of $ loor{-3}$?

The ceiling function $ig floor x ig floor$ for $x = -1.4$ is equal to ______.

Match the following values with their respective functions (floor and ceiling):

What is the output of the ceiling function $ig floor 1.5 ig floor$?

What type of correspondence is described by both one-to-one and onto functions?

The inverse of a bijective function is uniquely determined.

What is the value of the floor function $ lloor 2.8 floor$?

For a function 𝑓: 𝐴→𝐵, the composition of 𝑓 and its inverse is the __________ function.

Match the following function types with their definitions:

Which of the following best describes the ceiling function?

If x is an integer, then $ lloor x floor = x$.

What is the result of the ceiling function $ ceil -2.3 ceil$?

How many subsets does a set containing 5 elements have?

The set of negative numbers can be considered a universal set for all sets of natural numbers.

What is the correct power set for the set A = {1, 2, 3}?

The subset that contains only the element 9 and 5 from the universal set U = {1, 3, 5, 7, 9, 11, 13} is ______.

Match the following sets with their characteristics:

What is the value of the floor function for $-3.2$?

The ceiling function of $1.5$ is equal to 2.

What is the value of the ceiling function for $-1.4$?

The value of the floor function $ loor{2}$ is ______.

Match the numerical value with the correct function output (floor or ceiling):

Which of these values represents the ceiling function output for $1.5$?

The floor function for any integer $x$ is equal to $x$.

What is the value of floor function $ loor{-3}$?

What is a defining characteristic of a finite sequence?

A geometric progression has a common difference between its consecutive terms.

What is the common ratio of the geometric sequence 1, 2, 4, 8, 16, 32?

In an arithmetic progression, the common difference of the sequence 11, 7, 3, -1, -5, -9 is _____ .

Match the following types of sequences with their characteristics:

Which of the following is an example of an infinite sequence?

An arithmetic sequence can have a common ratio.

What is the last term of the finite sequence 2, 4, 6, 8, 12, 14?

What represents the operation of conjunction in Boolean algebra?

The Boolean product of two matrices uses addition and multiplication as defined in standard matrix operations.

What is the common operation used to replace multiplication in the Boolean product of matrices?

For two functions, $f$ and $g$, it holds that $f ullet g = g ullet f$.

What is the value of $loor{-3.2}$?

What is the output of $loor{1.5}$?

$loor{x} = x$ if and only if $x$ is an integer.

What is the value of $loor{-1.4}$?

What is the value of $loor{-3}$?

The ceiling function $ig floor x ig floor$ for $x = -1.4$ is equal to ______.

What is the output of the ceiling function $ig floor 1.5 ig floor$?

What is the value of the floor function $lloor 2.8 floor$?

If x is an integer, then $lloor x floor = x$.

What is the result of the ceiling function $ceil -2.3 ceil$?

The value of the floor function $loor{2}$ is ______.

What is the value of floor function $loor{-3}$?

The resulting matrix from the Boolean product of two matrices is defined using the operations _ and _.

What is the value of $loor{-1.4}$?

$loor{x} = x$ if and only if $x$ is an integer.

What is the output of the ceiling function $ig floor 1.5 ig floor$?

The value of $loor{-3.2}$ is ______.

What is the value of $ig floor 2 ig floor$?

What is the value of $loor{1.5}$?