Sets and functions, theoretical calc homework?

[concon]

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?

 

[SammyS]

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.