Question

PROVE A=(AUB)∩A

Answer 1

I am not going to attempt a "mathematical proof" rather I will state a few observations.

Suppose you have a universal set U containing the two sets A and B. Which means that A and B are subsets of U. "A U B" in this case represents a set containing the elements of both A and B.

For example

A={1,2,3}
B={2,4,5}

Then Z = A U B = {1,2,3,4,5}

Taking Z ∩ A = {1,2,3} ( since we are supposed to get the elements that are common between the two sets through the intersection operator)

You can try showing this using Venn diagrams if you have gone through them. That would be the easiest thing to do.