- #1

- 65

- 0

## Homework Statement

Let A,B, and C be subsets of universal set U. Prove the following

A. If U=A union B and intersection of A and B is not an empty set, then A= U\B

B. A\(B intersection C) = (A\B) union (A\C)

## Homework Equations

no relevant equations required

## The Attempt at a Solution

A.

So I know A union B = {x: (xεA) or (xεB)}

But I am having trouble on where to go from there. Intuitively I can see that the claim is true, but how do I prove this? step by step please

B.

I know that B intersection C= : {x: (xεB) and (xεC)}

A\B = {x: (xεA) and ~(xεB)}

A\C = {x: (xεA) and ~(xεC)}

Same problem as part a how do I prove this?