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 $B = B_1\cup B_2$
Cross Products Problem
1
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elementary-set-theory
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1This question should come with the hypothesis that neither A nor B are empty. – 2012-09-27
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0@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