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

proof:

Assume (x,y) is an element of A X (B U C). This means x is an element of A and y is an element of B or y is an element of C. Since (x,y) can be x as an element of A and y as an element of B, (x,y) is an element of A X B. Since (x,y) can also have x as an element of A and y as an element of C, (x,y) is an element of A X C.

A X (B-C)= (A X B) - (A X C)

not sure

A X (B intersect C)= (A X B) intersect (A X C)

please help with these proofs im not sure how the form of proofs about cartesian products should be