Let * be a binary operation on the set Q of rational numbers as follows:

Question 1

(i) a b = a − b (ii) a b = a2 + b2
(iii) a b = a + ab (iv) a b = (a − b)2
(v) ab=ab/4 (vi) a b = ab2

Find which of the binary operations are commutative and which are associative.

Question 2

(i) On Q, the operation is defined as a b = a − b. It can be observed that:

Thus, the operation * is not associative.

Hence, the operations defined in (ii), (iv), (v) are commutative and the operation defined in (v) is associative.

kratos · Answer 1 · 2020-07-07T09:59:15+0000

(i) On Q, the operation is defined as a b = a − b. It can be observed that:

Thus, the operation * is not associative.

Hence, the operations defined in (ii), (iv), (v) are commutative and the operation defined in (v) is associative.

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