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For each opertion ** difined below, determine whether ** isw binary, commutative or associative. (i) On Z, define a **b =a - b (ii) On Q, define a **b =ab +1 (iii) On Q, define a **b = (ab)/( 2) (iv) On Z ^(+), define a **b = 2 ^(ab) (v) On Z ^(+), define a **b=a ^(b) (vi) On R - {-1}, define a **b= (a)/( b +1) |
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Answer» (II) `**` is binary, commutative but not associative (iii) `**` is binary, both commutative and associative (iv) `**` is binary, cimmutative but not associative (v)` **` is binary but neither commutative nor associative (VI) `**` not binary |
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