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For each binary operation ** defined below, determine whether ** is commutative or associative on Q, define a**b=ab+1

Answer»

SOLUTION :`a**b=ab+1`
`b**a=ba+1=a**b``a,b in Q`
`THEREFORE **` is COMMUTATIVE
Since `(1**2)**3=(1xx2+1)**3`
`3**3=3xx3+1=10` and
`1**(2**3)=1**(2xx3+1)
`=1**7=1xx7+1=8`,
`(1**2)**3 ne 1**(2**3)`
`therefore **` is not associative


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