Question

use the following information to answer the next two questions.
let the universal set u = {natural numbers less than 13}
the following are subsets of the universal set u
a = {natural numbers less than 10}
b = {b | b = 3x, 1 ≤ x ≤ 4, x ∈ n}
c = {2, 4, 6, 8}

1. the elements in the set equivalent to (a ∩ b) ∪ c are

a. {2, 3, 4, 6, 8, 9}
b. {2, 4, 6, 8}
c. {3, 6, 9}
d. {6}

1. which of the following statements is true?

a. n(b) = 3
b. b ⊂ a
c. a ∩ b ∩ c = ∅
d. b = {1, 2, 4, 5, 7, 8, 10, 11}

Explanation:

Step1: Define universal set U

$U = \{1,2,3,4,5,6,7,8,9,10,11,12\}$

Step2: Define set A

$A = \{1,2,3,4,5,6,7,8,9\}$

Step3: Define set B

$B = \{3,6,9,12\}$

Step4: Define set C

$C = \{2,4,6,8\}$

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For Question 1:

Step5: Find $A \cap B$

$A \cap B = \{3,6,9\}$

Step6: Find $(A \cap B) \cup C$

$(A \cap B) \cup C = \{2,3,4,6,8,9\}$

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For Question 2:

Step7: Verify Option A

$n(B)=4
eq 3$, so false.

Step8: Verify Option B

$12 \in B$ but $12
otin A$, so $B
subseteq A$, false.

Step9: Verify Option C

$A \cap B \cap C = \{6\}
eq \emptyset$, so false.

Step10: Verify Option D

$B' = U - B = \{1,2,4,5,7,8,10,11\}$, so true.

Answer:

1. A. {2, 3, 4, 6, 8, 9}
2. D. $B'=\{1,2,4,5,7,8,10,11\}$