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