# Show by simplification

1. Sep 11, 2006

Hi,

with my special notation:
I- intersection

Can we prove that:
(A I B) subset of A by simplification from the rule of inference

since A I B -->A ??

If not, please can I have some suggestions?
B

2. Sep 11, 2006

### 0rthodontist

Sort of--that logical rule applies only to logical statements, not directly to sets. It says that you can conclude X from the statement X AND Y. The standard way to prove that $$A \cap B \subseteq A$$ starts by decomposing it into logical statements.
Assume $$x \in A \cap B$$
Then $$(x \in A) \vee (x \in B)$$
You can finish it

3. Sep 13, 2006