(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A,B,C,D are sets.

Prove that if C is contained in A and D is contained in B, then C∩ D is contained in A∩ B.

2. Relevant equations

3. The attempt at a solution

Let x be any element.

Then There exists (x that belongs to C∩D) and (x does not belong to A∩ B)

So x belongs to C and x belongs to D

If x belongs to C, since C is contained in A, then x belongs to A.

If x belongs to D, since D is contained in B, then x belongs to B.

So x belongs to A intersect B, a contradiction.

Then the original statement is true.

Is it okay?

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# Can you check this proof please: sets?

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