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Questions and Answers
What is a member or element of a set denoted by?
∈
What is the set A of vowels in the English alphabet?
{a, e, i, o, u}
Set B = {even numbers from 1 to 10} is well-defined.
True
What elements are included in set B = {whole numbers less than 5}?
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Match the following sets to their definitions:
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The cardinality of set F = {1, 2, 3, 4, 5} is denoted by ____.
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Which of the following sets is considered an infinite set?
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Two sets are equal if they contain the same elements.
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In interval notation, what does [4, 8] represent?
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{x 𝓔 ℝ /-3 < x < 6} has elements that are ____.
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Study Notes
Sets and their Representation
- Sets are collections of well-defined objects, usually represented by capital letters.
- Sets are denoted by braces and commas, containing their elements.
- An object belonging to a set is called a member or element, denoted by the symbol ∈.
- A set is well-defined if we know exactly if an object belongs to it.
- A variation of notation using ellipses (...) can be used to describe large sets, indicating "and so forth".
- Sets are denoted by braces
{}, commas,, and the symbol∈which means "is an element of".
Describing Sets
- Listing Method/ Roster Method: listing all elements enclosed in braces.
-
Rule Method/ Set-Builder Notation: descriptive phrase in braces, defining set elements. Example:
A = {x/x is an even number less than 5} -
Interval Notation: uses brackets
[]and parentheses()to represent ranges on a number line. Square brackets indicate inclusion (≤), and parentheses indicate exclusion (<).
Types of Sets
-
Empty Set: contains no members, denoted by
{}or the Danish letter∅. - Finite Set: has a countable number of elements, meaning you can list all elements.
- Infinite Set: has an uncountable number of elements, impossible to list all elements.
Cardinality of a Set
-
Cardinality: the number of elements in a set, denoted by
|A|orn(A). -
Example: If
F = {1, 2, 3, 4, 5}, thenn(F) = 5.
Equal and Equivalent Sets
- Equal Sets: have exactly the same elements.
- Equivalent Sets: have the same number of elements.
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Description
Explore the fundamental concepts of sets, their representations, and the methods for defining them. This quiz delves into different notations such as listing, set-builder, and interval notations, providing clarity on how to describe and work with sets effectively.
