Set Theory - Proving Contrapositive

[rooski]

Homework Statement

using set theroetic notation, write down and prove the contra-positive of:

GOD WHAT IS WRONG WITH LATEX? It is completely ruining my set notation! And i can't fix it!

If $$B \cap C \subseteq A$$ Then $$(C-A) u (B-A)$$ is empty.

The Attempt at a Solution

I'm awful with set notation and finding inverses of things. Here's my guess at what the contra-positive is:

if $$B \cup C \notin A$$ then $$( C - A ) \cup ( B - A )$$ is empty

 

[Outlined]

deleted

 

[vela]

The contrapositive of p→q is (not q)→(not p). Try again.

 

[rooski]

Hmm.

If B $$\cap$$ C is not a subset of A then (C-A) U (B-A) is not empty

is that the contrapositive?

 

[vela]

No. Note the order of p and q switch in the contrapositive.

Original statement: If X is a dog, X has four legs.
Contrapositive: If X does not have four legs, X is not a dog.

 

[rooski]

If (C-A) U (B-A) is not empty then B $$\cap$$ C is not a subset of A.

I think that's right. unless i did something wrong with inverting the logical statements.

 

[vela]

That's correct.