Question

if a×b is not an empty set and a×b is a subset of c×d, then prove that a is a subset of c and b is a subset of d​

Answer 1

Answer:

Step-by-step explanation

Suppose A x B is a subset of C x D. Let a be an arbitrary element of A and let b be an arbitrary element of B. Then (a, b) is an element of A x B.  Since A x B is a subset of C x D,  (a, b) is an element of C x D. Therefore a is an element of C and b is an element of D.  Since a and b were arbitrary elements of A and B, respectively, this shows that A is a subset of C and B  is a subset of D.

Note :

Arbitrary : (of a constant or other quantity) of unspecified value.