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.