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If $A_1 \times B_1 \cup A_2 \times B_2 = A \times B $ then show that $ A = A_1 \cup A_2$ and $B = B_1\cup B_2$

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    This question should come with the hypothesis that neither A nor B are empty.2012-09-27
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    @Jason: In fact it requires the hypothesis that none of the sets $A,B,A_1,B_1,A_2,B_2$ be empty.2012-09-27

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