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(a) Let '**' be a binary operation defined on Q, the set of rational numbers, as follows : (i) a**b=a-b, for a,binQ (ii) a**b=a^(2)+b^(2), for a,binQ (iii) a**b=a+ab, for a,binQ (iv) a**b=(a-b)^(2), for a,binQ (v) a**b=(ab)/(4), for a,binQ (vi) a**b=ab^(2), for a,binQ. Find which of the binary operations are commutative and which are associative. |
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