Set Operations: Intersection and Union

What is the cardinality of the set {2, 4, 6, 8}?

Which of the following symbols is used to denote 'is an element of' in set theory?

True or False: -5 is an element of the set {5, 10, 15, 20, 25}.

Which notation represents the cardinal number of a set?

In set builder notation, what does the expression {x | x is an even counting number less than 10} mean?

Which symbol is used to denote 'is not an element of' in set theory?

What is the intersection of sets {1, 3, 5} and {2, 4, 6}?

What is the union of sets {1, 3, 5} and {3, 4, 5}?

If A = {m, n}, B = {n, o}, and C = {a, b}, what is (A ∪ B) ∩ C?

What is the symmetric difference between sets {1, 2, 3} and {2, 3, 4}?

Given A = {p, q}, B = {q, r}, and C = {p, r}, what is (A ∪ B) - (B ∩ C)?

If U = {1, 2, 3, 4}, A = {1, 2}, and B = {2, 3}, what is the complement of (A ∪ B)?

What is the symmetric difference, A  B, defined as?

In Venn Diagrams, what does shading represent?

What is U – (A  B) equal to?

What is meant by (A  B)  C on a Venn diagram?

What is A – B equivalent to?

Which statement represents B'?

Set Theory Basics

The cardinality of the set {2, 4, 6, 8} is 4.
The symbol "∈" is used to denote "is an element of" in set theory.
The statement "-5 is an element of the set {5, 10, 15, 20, 25}" is False.
The cardinal number of a set is represented by the notation "| |" or "card()".

Set Builder Notation

The expression {x | x is an even counting number less than 10} means the set of all even counting numbers less than 10.

Set Operations

The symbol "∉" is used to denote "is not an element of" in set theory.
The intersection of sets {1, 3, 5} and {2, 4, 6} is the empty set, ∅.
The union of sets {1, 3, 5} and {3, 4, 5} is the set {1, 3, 4, 5}.
(A ∪ B) ∩ C = ∅, given A = {m, n}, B = {n, o}, and C = {a, b}.
The symmetric difference between sets {1, 2, 3} and {2, 3, 4} is the set {1, 4}.
(A ∪ B) - (B ∩ C) = {p, r}, given A = {p, q}, B = {q, r}, and C = {p, r}.
The complement of (A ∪ B) is {3, 4}, given U = {1, 2, 3, 4}, A = {1, 2}, and B = {2, 3}.
The symmetric difference, A ∆ B, is defined as (A ∪ B) - (A ∩ B).

Venn Diagrams

Shading in Venn Diagrams represents regions of the sets.
U – (A ∩ B) is equal to the region of U not in the intersection of A and B.
(A′ ∩ B′) ∩ C on a Venn diagram represents the region of C that is not in A and not in B.
A – B is equivalent to A ∩ B′.

Test your understanding of set operations, specifically intersection and union. Determine the resulting sets when given specific sets to intersect or union.