Q. 55.0( 4 Votes )

If A × B C × D and A × B ≠ ϕ, prove that A C and B D.

Answer :

Given: A × B C × D and A × B ≠ ϕ


Need to prove: A C and B D


Let us consider, (x, y) (A × B) ---- (1)


(x, y) (C × D) [as A × B C × D] ---- (2)


From (1) we can say that,


x A and y B ---- (a)


From (2) we can say that,


x C and y D ---- (b)


Comparing (a) and (b) we can say that,


x A and x C


A C


Again,


y B and y D


B D [Proved]


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RS Aggarwal - Mathematics