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Let A={1,2},B={3,4}" and "C={4,5}. We ...

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

Text Solution

Verified by Experts

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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