Question

a) For any three sets A, B and C, Prove that
Ax(BUC)=(A*B) U(A*C).​

Answer 1

Step-by-step explanation:

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)