Question

Can you conclude that a = b if a, b, and c are sets such that a ∩ c = b ∩ c?

1) True
2) False

Answer 1

We cannot conclude that a = b based on the given information that a ∩ c = b ∩ c. The correct answer is False.

Step-by-step explanation:

We cannot conclude that a = b based on the given information that a ∩ c = b ∩ c. The intersection of sets a and c being equal to the intersection of sets b and c only tells us about the elements that are common to both sets. It does not provide enough information to determine if the sets a and b are equal. There could still be elements in a or b that are not in the intersection with c. Therefore, the correct answer is 2) False.