Exploring Sets in Mathematics

What is the set notation for the set of all even numbers?

• { x ∈ ℤ | x = 2n, n ∈ ℤ }

• { x ∈ ℤ | x = 2n + 1, n ∈ ℤ }

• { x ∈ ℤ | x = 3n, n ∈ ℤ }

• { x ∈ ℤ | x = n^2, n ∈ ℤ }

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

• {1, 2, 4}

• {1, 4}

• {2, 3, 4}

• {2, 3}

Determine if {a, b} is a subset of {a, b, c, d}.

• Yes

• No

• {a, d}

• {a, b, c}

If C = {x | x is a prime number less than 10}, list the elements of C.

• [2, 3, 5, 7]

• [2, 3, 5, 9]

• [1, 4, 6, 8]

• [2, 3, 4, 5]

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

• {2, 3, 5}

• {1, 2, 3, 4, 5}

• {1, 2, 3}

• {3, 4}

If D = {1, 2, 3, 4} and E = {2, 3}, is E a subset of D?

• Yes, E is a subset of D.

• E contains elements not in D.

• E is equal to D.

• No, E is not a subset of D.

Solve: If A = {x | x is a student in class}, and B = {x | x is a student in the school}, is A a subset of B?

• Yes, A is a subset of B.

• A is a proper subset of B.

• No, A is not a subset of B.

• A and B are disjoint sets.

What is the complement of the set {1, 2, 3} in the universal set U = {1, 2, 3, 4, 5, 6}?

• {4, 5, 6}

• {3, 4}

• {5, 6}

• {1, 2}

If F = {2, 4, 6} and G = {1, 2, 3}, what is F ∪ G?

• {1, 2, 3, 4, 6}

• {1, 3, 4, 6}

• {2, 4}

• {1, 2, 3}

How many subsets does the set {a, b, c} have?

• 4

• 8

• 10

• 6