- #1

workerant

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## Homework Statement

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.

## Homework Equations

## 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?