Question

A U (B n C) = (A U B ) n (A U C)

Answer 1

Step-by-step explanation:

Let x be an arbitrary element in B

So x is in AUB (as B is a subset of AUB)

So x is in AUC (as AUB = AUC)

So x is in A or x is in C

If x is in C, then we are done

So let x be in A

So x is in AnB (as x was originally in B, not it is in A as well)

So x is in AnC (as AnB = AnC)

So x is in C (as AnC is a subset of C)

As x was an arbitrary element of B, B is a subset of C

Similarly C is a subset of B

Hence, B = C (as both are subsets of each other)