# Proving a subset

## Homework Statement

The problem I have been given is to prove (A - B) U C is than less or equal to (A U B U C) - (A n B)

## The Attempt at a Solution

I've tried starting off with just (A-B) U C. Then I would say how x ε c or x ε (A - B). Also if x ε a, then x ε c and x is not in b. If x ε c, since c is a subset of (A U B U C) , x ε (A U B U C). I don't know if this is right or where to go from here.

Mark44
Mentor

## Homework Statement

The problem I have been given is to prove (A - B) U C is than less or equal to (A U B U C) - (A n B)
This is a statement about sets, so the relationship is $\subseteq$, not ≤.

## The Attempt at a Solution

I've tried starting off with just (A-B) U C. Then I would say how x ε c or x ε (A - B). Also if x ε a, then x ε c and x is not in b.
Try to be more careful with the names of the sets, which are A, B, and C, not a, b, and c.
If x ε c, since c is a subset of (A U B U C) , x ε (A U B U C). I don't know if this is right or where to go from here.

i'd say that u can use:

AUBUC= lAl + lBl + lCl - lBnCl - lAnBl - lAnCl+lAnBnCl

but i'm not 100% positive just trying to give some help :)

My professor said we can also try to prove or find a counterexample to this statement. Let A, B and C be sets. Then (A-B) U C = (A U B U C) - (A n B). I'm not really sure what she means by counterexample.

HallsofIvy