Let A and B be sets. Show that ( A ∩ B) ⊆ A. Prove first the left side ⊆ right side. Then right side ⊆ left side.
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Is this a true statement $\displaystyle x\in A\rightarrow x\in A?$
yes
So if $\displaystyle x\in A\cap B$ then $\displaystyle x\in A\text{ and }x\in B$. Thus ?
Then they are subsets
You don't need to prove right to left, and we can't anyway.
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).
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