1.

Let A={1,2},B={3,4}" and "C={4,5}. We have verify that (AxxB)xxC=Axx(BxxC) and hence find AxxBxxC.

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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