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Let A={1,2},B={3,4}" and "C={4,5}. We have verify that (AxxB)xxC=Axx(BxxC) and hence find AxxBxxC. |
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Answer» SOLUTION :We have `AxxB={1,2}XX{3,4}={(1,3),(1,4).(2,3),(2,4)}` `implies""(AxxB)xxC={(1,3),(1,4),(2,3),(2,4)}xx{4,5}` `={(1,3,4),(1,3,5),(1,4,4),(1,4,5),(2,3,4),(2,3,5),(2,4,4),(2,4,5)}.` Again, `BxxC={3,4}xx{4,5}={(3,4),(3,5),(4,4),(4,5)}` `implies""Axx(BxxC)={1,2}xx{(3,4),(3,5),(4,4),(4,5)}` `={(1,3,4),(1,3,5),(1,4,4),(1,4,5),(2,3,4),(2,3,5),(2,4,4),(2,4,5)}.` `:.""(AxxB)xxC=Axx(BxxC)=AxxBxxC.` HENCE, `(AxxBxxC)={(1,3,4),(1,3,5),(1,4,4),(1,4,5),(2,3,4),(2,3,5),(2,4,4),(2,4,5)}.` |
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