# If A × B <span la

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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