# Sets and functions, theoretical calc homework?

## 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?

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## 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?
Hello concon,

Welcome to PF !

We don't do step by step solutions here at PF, if that's what you're asking for.

It looks to me that A is not true.

In general, to show that two sets are equal, i.e. D = E, show that D is a subset of E and E is a subset of D.
To show that set D is a subset of E:
Let xεD. Then show that it follows that xεE .
etc.