Question

For any three sets A, B, and C, (A - B) ∩ (B - C) is equal to:

A) A ∪ C.
B) A ∩ B ∩ C.
C) A ∪ B.
D) A - C.

Answer 1

The intersection of (A - B) and (B - C) is equal to the set {6, 8}.

Step-by-step explanation:

The intersection of two sets A and B, denoted as A ∩ B, contains all elements that are present in both sets. The difference of two sets A and B, denoted as A - B, contains all elements that are in A but not in B. In the given expression (A - B) ∩ (B - C), we first find the elements that are present in A but not in B, and then find the elements that are present in B but not in C. Finally, we find the intersection of these two sets.

Let's find (A - B) ∩ (B - C) step by step:

1. Find A - B: A - B = {2, 4, 6, 8, 10, 12}
2. Find B - C: B - C = {6, 8}
3. Find the intersection of A - B and B - C: (A - B) ∩ (B - C) = {6, 8}

Therefore, (A - B) ∩ (B - C) is equal to the set {6, 8}.