Exploring Set Theory Concepts

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

• { x ∈ ℤ | x = 2n + 1, n ∈ ℤ }

• { x ∈ ℤ | x = n^2, n ∈ ℤ }

• { x ∈ ℤ | x = 2n, n ∈ ℤ }

• { x ∈ ℤ | x = 3n, n ∈ ℤ }

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

• {1, 2, 3, 4}

• {1, 4}

• {1, 2, 3}

• {2, 3}

List all the subsets of the set {a, b}.

• {a, b, c}

• {b, c}

• {a, b}

• [{}, {"a"}, {"b"}, {"a", "b"}]

Are the sets {x, y} and {y, x} equal? Why or why not?

• No, the sets are different because of the order.

• Yes, but only if x and y are the same element.

• No, sets cannot contain duplicate elements.

• Yes, the sets {x, y} and {y, x} are equal.

Define a null set and provide an example.

• An example of a null set is {1, 2, 3}.

• A null set contains at least one element.

• An example of a null set is ∅ or {}.

• A null set is a set with infinite elements.

If C = {1, 2}, what is the subset of C that contains only the number 1?

• {2}

• {1}

• {1, 2}

• {}

What is the union of the sets {a, b} and {b, c}?

• {a, b, c}

• {a, b, c, d}

• {b}

• {a, c}

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

• D is a proper subset of E.

• D and E are equal sets.

• No, D is not a subset of E.

• Yes, D is a subset of E.

What is the notation for the null set?

• ∅

• null

• []

• {}

If F = {x | x is a prime number less than 10}, what are the elements of F?

• [2, 3, 5, 7]

• [2, 3, 5, 11]

• [2, 3, 5, 9]

• [1, 4, 6, 8]