Set Theory 2.2 B

• The set A={x∣x∈N, x is less than 20, and x is divisible by both 3 and 4} in word form is:

• A is the set of all natural numbers less than 20 that are only divisible by 3.

• A is the set of all natural numbers less than 20 that are only divisible by 4.

• A is the set of all natural numbers less than 20 that are divisible by both 3 and 4.

• • A is the set of all natural numbers only divisible by 12.

Are the sets A = {2, 4, 4, 6, 8, 8} and B = {8, 6, 6, 4, 2, 2} equal?

Choose two.

• No, because the elements are in a different order.

• No, because set A has repeated elements.

• Yes, because they contain the same elements regardless of order and repetition.

• Yes, because they both contain 6 elements.

• The set C={5,6,7,8} using set-builder notation is:

• Choose two.

• {x ∣ x ∈ N and 5< x < 8}

• {x ∣ x ∈ N and 5≤ x < 8}

• {x ∣ x ∈ N and 5 < x ≤ 8}

• • {x ∣ x ∈ N and 5 ≤ x ≤ 8}

• • {x ∣ x ∈ N and 4< x < 9}

   

• Let D = {1,3,5,7,9}.

• Which of the following statements is true?

• 2 ∈ D

• • 5 ∉ D

• 2 ∉ D and 5 ∈ D

• 2 ∈ D and 5 ∉ D

• The set E = {x ∣ x ∈ N and x > 0} is:

• The set of negative integers.
• The set of all integers.
• The set of rational numbers.
• The set of positive integers.

Set B is defined as {x ∣ x ∈ N, 10 ≤ x < 70, and x ≠ 51 to 55}. The cardinality of B is:

• 50
• 60
• 55
• 70

• Set C is defined as {x ∣ x ∈ N, x≤ 100, x ≠ 10 to 20}. The cardinality of C is:

• 90
• 75
• 85
• 89

• The set G = {x ∣ x ∈ N and 75 ≤ x < 950} in roster notation is:

• {70, 71, 72, ..., 74}
• {950, 951, 952, ..., 1000}
• {75, 76, 77, ..., 100}
• {75, 76, 77, ..., 949}
• {0, 1, 2, ..., 74}

• The set F = {x ∣ x ∈ N and x is even} is:

• The set of all odd integers.

• The set of all natural numbers.

• The set of all even integers.

• The set of all prime numbers.

Set H is defined as {x ∣ x ∈ N, 1 ≤ x < 50, and x ≠ 25 to 30}. The cardinality of H is:

• 42

• 40

• 50

• 45