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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- Oct 12th 2010, 08:01 AMlm6485Set 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 AMPlato
Is this a true statement $\displaystyle x\in A\rightarrow x\in A?$

- Oct 12th 2010, 09:24 AMlm6485
yes

- Oct 12th 2010, 09:28 AMPlato
So if $\displaystyle x\in A\cap B$ then $\displaystyle x\in A\text{ and }x\in B$. Thus ?

- Oct 13th 2010, 09:55 AMlm6485
Then they are subsets

- Oct 13th 2010, 10:17 AMMoeBlee
You don't need to prove right to left, and we can't anyway.

- Oct 13th 2010, 10:19 AMMoeBlee