SOLUTION: Prove by identity A u (A n B)= A

Question 1040074: Prove by identity
A u (A n B)= A
Found 2 solutions by ikleyn, robertb:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
Prove an identity
A u (A n B)= A
~~~~~~~~~~~~~~~~~~~~

Let x be any element from the left side set. Then x belongs to A, to the right side set.

Let y be any element of A, which is right side set. Then y belongs to the left side set.

Thus we proved that every element of the left side set belongs to the right side set, and opposite,
that every element of the right side set belongs to the left side set.

It means that the two sets are equal.

The proof is completed.

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
(A u A) n (A u B), by the distributive property,
= A n (A u B), since A u A = A.
= A, since A is a subset of A u B.

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