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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4 comments:
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Thanks..
Thank u so much 🤩🤩🤩
you saved my precious time to prove this ... thank you 🔥🙂
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