AUB MEANS ALL AREA UNDER A AND B ..AND COMPLEMENT ALL THE AREA IN UNIVERSAL SET OUT OF A AND B ...NOW SINCE (AUB)' IS AREA OUT OF A AND B SO THERE NOTHING COMMON BETWEEN (AUB)' AND A HENCE...(AUB)'intersectiona= phi
consider A ={1234} B ={2345} then A^[AUB] is A union B consists of all elements of A and B and its complement is some set of elements like {6789} this set and A set complement is automatically 0 elements ie pie always use examples in sets
Let U stand for union and | stand for intersection and Pi stands for the null set as i cannot write the usual symbols.Solution is as follows:
A | (A U B)' = A | (A' | B') = (A | A') | B' = Pi | B' = Pi
Explanation: Apply the usual formula for the compliment and the next as intersection holds associative law calculate the intersection of A and A' which is a null set and hence the answer follows.