Question

Given the following sets:
𝐴 = {2, 4, 6, 8, 10, 12}
𝐵 = {8, 10, 12, 14, 16, 18}
𝐶 = {7, 8, 9, 10 11, 12, 13}
(𝐴 ∩ 𝐵) ∪ (𝐵 ∩ 𝐶) is

• A. {8, 10, 12, 14}
• B. {8, 10, 12}
• C. {7, 8, 10, 11, 12, 13, 14}
• D. {4, 6, 7, 8 10, 11, 12, 13}

Answer 1

The Correct Option is B

To solve this problem, we need to find the union of two sets: \( (A \cap B) \) and \( (B \cap C) \).

1. Intersection of Set A and Set B: 

Set \( A = \{2, 4, 6, 8, 10, 12\} \) and Set \( B = \{8, 10, 12, 14, 16, 18\} \).

The intersection \( A \cap B \) includes all elements common to both sets A and B.

\( A \cap B = \{8, 10, 12\} \).

1. Intersection of Set B and Set C:

Set \( B = \{8, 10, 12, 14, 16, 18\} \) and Set \( C = \{7, 8, 9, 10, 11, 12, 13\} \).

The intersection \( B \cap C \) includes all elements common to both sets B and C.

\( B \cap C = \{8, 10, 12\} \).

1. Union of Intersections:

The union of \( A \cap B \) and \( B \cap C \) combines all elements from both intersections, without repeating any elements.

\( (A \cap B) \cup (B \cap C) = \{8, 10, 12\} \cup \{8, 10, 12\} = \{8, 10, 12\} \).

Since both intersections are identical, the union remains the same set of elements.

Conclusion: The result of the operation \( (A \cap B) \cup (B \cap C) \) is the set \(\{8, 10, 12\}\). Therefore, the correct option is

{8, 10, 12}

.