Let A and B be nonempty sets and let c and D be sets If A ti

Let A and B be nonempty sets and let c and D be sets. If A times B C times D, then A C and B D. Proof? The proof is the same as the one presented in Exercise 19.

Solution

SOLUTION ;-

Let a be any element of A (a A )and Let b be any element of B (bB).

Then (a,b) A×B

SInce A×B C×D , then the elements of A and B belongs to C and D

i.e, (a,b) C×D

Hence a C and b D

Therefore A C and B D.