Question

what can you say about the sets a and b if we know the following:- (12 points) a) a ∪ b = a? b) a ∩ b = a? c) a − b = a? d) a − b = b − a?

Answer 1

If the given statements hold true, set B is a subset of set A, set A is a subset of set B, set B is an empty set, and sets A and B are equal.

Step-by-step explanation:

To analyze the given statements, let's break them down one by one:

a) If A ∪ B = A, it means that the union of sets A and B is equal to set A. This implies that all elements in set B are already included in set A. Therefore, set B is a subset of set A.

b) If A ∩ B = A, it means that the intersection of sets A and B is equal to set A. This implies that all elements in set A are also present in set B. Therefore, set A is a subset of set B.

c) If A - B = A, it means that the set difference of A and B is equal to set A. This implies that all elements in set B are not present in set A. Therefore, set B is an empty set.

d) If A - B = B - A, it means that the set difference of A and B is equal to the set difference of B and A. In other words, both sets have the same elements. Therefore, set A and set B are equal.