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## Homework Statement

Prove the absorption law A U (A and B) = A

## Homework Equations

## The Attempt at a Solution

I need to prove the sets are equal.

I don't know how to prove the right hand as a subset of the left hand.

For left hand as subset of right hand, it's pretty simple (we can define a new called G holding x in A and in B), and G is subset of A, then G U A is A (definition of subset and Union).

But how do I prove the right hand?

I started writing "There exists a set A...." and I thought about using partition, but then I couldn't go on anymore. If I say there exists an arbitrary set B, and x in A and B, then I am again writing the first proof.

Can someone please help me? Thanks.