Can Simplification Prove (A I B) Subset of A using Special Notation?

[brad sue]

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

 

[0rthodontist]

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

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

 

[brad sue]

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

OK I understand what to do.
Thank you