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Question

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

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Solution

Let: (x, y) (A×B) xA, yBNow,(A×B)(C×D) (x,y) (C×D) Or, xC and y DThus, we have: AC & BD

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