Exploring Set Theory Concepts

What is the result of A ∪ B if A = {1, 2} and B = {2, 3}?

• {1, 3}

• {1, 2, 2, 3}

• {2}

• {1, 2, 3}

If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?

• {2}

• {6}

• {3}

• {4}

Define the difference of two sets A and B, denoted as A - B.

• A - B = { x | x ∉ A and x ∉ B }

• A - B = { x | x ∈ B and x ∉ A }

• A - B = { x | x ∈ A }

• A - B = { x | x ∈ A and x ∉ B }

If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∩ B?

• {3}

• {1, 2, 3, 4, 5}

• {1, 2}

• {4, 5}

What is the power set of A = {a, b}?

• { {}, {a}, {b}, {a, b} }

• {a, {b}}

• {a, b}

• {a, b, c}

If A = {1, 2, 3} and B = {1, 2, 3}, are A and B equal? Why or why not?

• No, A and B are equal only if they are subsets of each other.

• Yes, A and B are equal.

• Yes, A and B are equal but only in terms of their size.

• No, A and B are not equal because they have different elements.

What is the complement of set A if the universal set U = {1, 2, 3, 4, 5} and A = {2, 3}?

• {2, 3, 4}

• {1, 4, 5}

• {1, 2, 3}

• {3, 4, 5}

If A = {1, 2} and B = {2, 3}, what is A ∪ (A ∩ B)?

• {1, 2, 3}

• {1, 2}

• {2, 3}

• {1, 3}

Explain the associative property of union in set theory.

• The associative property of union indicates that the intersection of sets is affected by grouping.

• The associative property of union only applies to finite sets and not to infinite sets.

• The associative property of union in set theory allows for the grouping of sets in union operations without affecting the outcome.

• The associative property of union states that the order of sets in a union operation matters.

If A = {x | x is a natural number less than 5} and B = {x | x is a natural number less than 3}, what is A - B?

• {1, 2, 3, 4}

• {2, 3, 4}

• {1, 2}

• {3, 4}