Prove that A X (B U C) = (A X B) U (A X C)

In English this is saying to prove that the Cartesian product of A and B union C is equal to the Cartesian product of A and B union the Cartesian product of A union C.

iff=if and only iff

Consider that the ordered pair (x,y) is an element of A X (B U C)

which is true iff x is an element of A and y is an element on (B U C)

iff x is an element of A and y is an element of B or y is an element of C

iff x is in A and y is in B or x is in A and y is in C

iff (x,y) is in A X B or (x,y) is in A X C

iff (x,y) is in (A X B) U (A X C)

thus A X (B U C) = (A X B) U (A X C)

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## 2 comments:

Super helpful! Thanks!

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