# Set Proofs

• Oct 12th 2010, 08:01 AM
lm6485
Set Proofs
Let A and B be sets. Show that ( A ∩ B) ⊆ A. Prove first the left side ⊆ right side. Then right side ⊆ left side.
• Oct 12th 2010, 08:13 AM
Plato
Is this a true statement $x\in A\rightarrow x\in A?$
• Oct 12th 2010, 09:24 AM
lm6485
yes
• Oct 12th 2010, 09:28 AM
Plato
So if $x\in A\cap B$ then $x\in A\text{ and }x\in B$. Thus ?
• Oct 13th 2010, 09:55 AM
lm6485
Then they are subsets
• Oct 13th 2010, 10:17 AM
MoeBlee
You don't need to prove right to left, and we can't anyway.
• Oct 13th 2010, 10:19 AM
MoeBlee
Quote:

Originally Posted by lm6485
Then they are subsets

Yes, but say specifically what you mean by "they", and say why "x in A and x in B" justifies that (it might be so obvious that you miss the need to say it).