Prove if true or give a counter example if false: For all sets A,B and C , A * (B U C) = (A* B) U (A* C):?

Prove if true or give a counter example if false:





For all sets A,B and C , A * (B U C) = (A* B) U (A* C):

Prove if true or give a counter example if false: For all sets A,B and C , A * (B U C) = (A* B) U (A* C):?
Well, if by "*" you mean intersection, its true.





Here's an informal proof. Suppose A is just those elemenst in A alone, B in B alone, C in C alone, AB those in A and B but not C, etc.





So A*(BuC) = AB and AC and ABC


A*B = AB and ABC


A*C = AC and ABC


So A*B u A*C = AB and AC and ABC


QED.


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