# How to prove it 3.3 exercise help please

1. Aug 18, 2013

### eddiep1993

I am currently reading vellemans how to prove it for the purpose of being able to construct a proof on my own. I would like to carry on this knowledge to also help me out with spivaks calculus So the problem is:

Prove that if a and b\c are disjoint, then a$\bigcap$b$\subseteq$c.
1.goal: a$\bigcap$b\c=∅ → a$\bigcap$b$\subseteq$c

2. Givens:a$\bigcap$b\c=∅ Goal:a$\bigcap$b$\subseteq$c

3.Givens:a$\bigcap$b\c=∅ x$\in$a x$\in$b Goal: x$\in$c
This is as far as I got. I haveE no idea where to go from here and I feel the solution is starting right at me. I think it might have something to do with the fact that a and b\c are disjoints. This might be in the wrong section but I don't no where else to put it

Last edited: Aug 18, 2013
2. Aug 18, 2013

### tiny-tim

hi eddiep1993! welcome to pf!
that's right

if x ε a, then x not ε in b/c …

carry on from there

3. Aug 24, 2013

### haruspex

Maybe: a$\bigcap$b\c=∅ x$\in$a x$\in$b x$\notin$c Goal: contradiction