Lecture Two: Set Theory

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Questions and Answers

Match the following set operations with their corresponding descriptions:

A' = The set of elements in the universal set that are not in A A ∩ B = The set of elements that belong to both A and B A ∪ B = The set of elements that belong to A or B or both A ⊄ B = Set A is not a subset of Set B

Match the following set operation symbols with their corresponding names:

∩ = Intersection ∪ = Union ' = Complement ⊄ = Not a subset of

Match the following set relationships with their corresponding Venn diagram representations:

Disjoint sets = Two circles that do not overlap Subset = One circle completely inside another Overlapping sets = Two circles that partially overlap

Match the following set notations with their corresponding verbal descriptions:

{x | x ∈ A and x ∈ B} = The intersection of sets A and B {x | x ∈ A or x ∈ B} = The union of sets A and B {x | x ∈ U and x ∉ A} = The complement of set A (A') {x | x ∈ A and x ∉ B} = The set of elements in A but not in B Signup and view all the answers

Match the following terms with their corresponding meanings in the context of sets:

Universal set = The set containing all possible elements Subset = A set whose elements are all contained within another set Element = A single item or member within a set Empty set = A set with no elements Signup and view all the answers

Match the following set operations with their corresponding examples using the sets A = {1, 2, 3} and B = {2, 4, 6}:

A ∩ B = {2} A ∪ B = {1, 2, 3, 4, 6} A' = {4, 5, 6, 7, ...} (assuming the universal set contains natural numbers) A ⊄ B = True, since not all elements of A are in B Signup and view all the answers

Match the following set operations with their corresponding graphical representations in a Venn diagram:

Intersection = The overlapping region of two circles Union = The entire area enclosed by both circles Complement = The area outside of a circle Disjoint sets = Two circles that do not intersect Signup and view all the answers

Match the following set operations with their corresponding symbolic representations:

Intersection = A ∩ B Union = A ∪ B Complement = A' Not a subset of = A ⊄ B Signup and view all the answers

Match the set notation with its meaning:

$A \subseteq B$ = A is a subset of B $x \in A$ = x is an element of A ${}$ or $\emptyset$ = An empty set U = Universal set Signup and view all the answers

Match the set type with its description:

Finite Set = A set with a countable number of elements Infinite Set = A set with an unlimited number of elements Null Set = A set that contains no elements Universal Set = A set containing all elements under consideration Signup and view all the answers

Match the examples with the type of set they represent:

{1, 2, 3, ..., 100} = Finite Set {1, 3, 5, ...} = Infinite Set {} = Null Set All fresh water lakes in a country = Universal set Signup and view all the answers

Match the set term with its corresponding description:

Element = An object contained within a set Set = A well-defined collection of distinct objects Subset = A set where all its elements are in another set Member = Synonym for element of a set Signup and view all the answers

Match the following set concepts to their descriptions:

A set is a collection of objects = A description of what constitutes a set The order of elements in a set does not matter = A property of sets A subset contains only elements within a larger set = Defines what a subset looks like Sets can be finite or infinite = A characteristic of sets in terms of size Signup and view all the answers

Match the term with its description in the context of Set Theory:

Set membership = Indicates that an element is part of a set Set inclusion = Indicates that one set is part of another Null set = A set that contains no elements Universal set = The set containing all specified elements Signup and view all the answers

Match the following descriptions with the correct set theory term:

A set with no elements. = Null Set A set that contains all possible elements of interest. = Universal Set A set within a larger set. = Subset An item within a set. = Element Signup and view all the answers

Match each concept with a statement that demonstrates it:

Finite Set = The set of days in a week. Infinite Set = The set of natural numbers. Subset = The set of even numbers is contained within the set of all integers. Element = The number 3 is a member of set {1,2,3,4}. Signup and view all the answers

Match the set notations with their descriptions:

$A \subset B$ = A is a subset of B $x \in A$ = x is an element of A $x \notin A$ = x is not an element of A $\emptyset$ = The null set Signup and view all the answers

Match the following set representations with their examples:

Descriptive Method = $P = {x | x = 0, 1, 2, ..., 7}$ Enumerative Method = $P = {0, 1, 2, 3, 4, 5, 6, 7}$ Set A = $A = {a, d, c, b}$ Set B = $B = {d, c, a, b}$ Signup and view all the answers

Match the set operations and relations with their meanings:

Equal sets = Two sets containing the same elements Subset = A set whose elements are all contained in another set Null Set = A set with no elements Universal Set (U) = A set that contains all the elements under consideration Signup and view all the answers

Given $B = {1, 2, 3, 4, 5}$, match the set descriptions with their results:

The set of all $x^2$ such that $x \in B$ = $C = {1, 4, 9, 16, 25}$ The set of all $4x + 1$ such that $x \in B$ = $D = {5, 9, 13, 17, 21}$ B is a subset of E = All elements of B are found in E The set of all prime numbers less than or equal to 5 = $A = {2, 3, 5}$ Signup and view all the answers

Match the general concepts in set theory with their descriptions:

Elements or members = Objects in a set Capital letters = Used to represent sets $\in$ = Symbol that means is a member of $\notin$ = Symbol that means is not a member of Signup and view all the answers

Match the characteristics with specific examples

$A = {a, b, c}$ and $B = {c, b, a}$ = Example of Equal sets $B={1, 2, 3, 4, 5}$ and $E={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$ = Example of a subset $\emptyset$ or {} = Example of a null set $A$ = {the set of all prime numbers ≤ 5} = A descriptive set Signup and view all the answers

Match the example with set theory concepts:

$A = {a, d, c, b}$ and $B = {d, c, a, b}$ = Equal sets $B \subset E$ = Subset of a set $2 \in A$ = Element of a set $4 \notin A$ = Not an element of a set Signup and view all the answers

Match the examples with the correct set type

$P = {x | 0 \leq x \leq 7}$ = Descriptive Method $P = {0, 1, 2, 3, 4, 5, 6, 7}$ = Enumerative Method $C = {1, 4, 9, 16, 25}$ = Derived set based on Elements of set B $D = {5, 9, 13, 17, 21}$ = Derived set based on Elements of set B Signup and view all the answers

Match the following set operations with their definitions:

M ∩ N = Intersection of sets M and N A U B = Union of sets A and B A ∩ A = Intersection of set A with itself A U ∅ = Union of set A with the empty set Signup and view all the answers

Match the following laws of set algebra with their corresponding examples:

Commutative Law = A U B = B U A Associative Law = A U (B U C) = (A U B) U C Distributive Law = A U (B ∩ C) = (A U B) ∩ (A U C) Further Law = A ∩ A' = ∅ Signup and view all the answers

Match the following set characteristics with their types:

Disjoint Sets = Sets with no elements in common Universal Set = The set containing all possible elements Null Set = The empty set denoted by Ø Subset = A set that contains some or all elements of another set Signup and view all the answers

Match the following terms with their definitions:

Complement of a set = Elements not in the set within the universal set Venn Diagram = Pictorial representation of sets and their relationships Element = An individual object in a set Union = Combining elements from two or more sets Signup and view all the answers

Match the following set notations with their meanings:

A U B = Elements that are in either set A or set B A ∩ B = Elements that are in both set A and set B A' = Complement of set A U = Universal set containing all elements Signup and view all the answers

Match the following statements with their correct assertions:

M ∩ N = Ø = Sets M and N are disjoint A U A = A = The union of set A with itself A ∩ U = A = Intersection of set A with the universal set A U A' = U = Union of a set and its complement is the universal set Signup and view all the answers

Match the following examples to their corresponding set operations:

A = {1, 3, 5} = Example of a set B = {3, 5, 7, 9} = Example of another set A ∪ B = Combining elements from sets A and B A ∩ B = Elements common to sets A and B Signup and view all the answers

Match the following types of sets with their characteristics:

Null Set = A set with no elements Single Element Set = A set containing only one distinct element Disjoint Set = Sets that do not share any elements Universal Set = The largest set that contains all other sets Signup and view all the answers

Flashcards

What is a set?

A collection of distinct objects.

Finite Set

A set with a limited number of elements, like the days of the week.