# Proof about Set Theory

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Let A, B, C be sets and let X be a set containing A, B, C as subsets.

Prove that A intersects (B union C)= (A intersects B) union (A intersects C)

A union (X relative complement of A)=X and A intersects (X relative complement of A)=empty set

X relative complement (A intersects B)=(X relative compliment of A) union (X relative compliment of B)

Please be as detailed as possible in solution. Thanks!

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Let A, B, C be sets and let X be a set containing A, B, C as subsets.

Prove that A intersects (B union C)= (A intersects B) union (A intersects C)

Proof: We need to prove

Let

and ...

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