Question

consider the binary operation * on quality defined by a*b=ab/6 show that * is commutative and associative
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Answer 1

Answer:

Commutative law, is satisfied when a*b = b*a

                                                   here, a*b = ab/6

                                                            b*a = ba/6 = ab/6

Therefore, a*b = b*a. Therefore, commutative law is satisfied.

Associative law, is satisfied when a*(b*c) = (a*b)*c

                                                    here, a*(b*c) = a*(bc/6)

                                                                           = abc/6 ----> (1)

                                                               (a*b)*c = (ab/6)*c

                                                                            = abc/6  -----> (2)

Since equations (1) and (2) are equal, associative law is satisfied.

Hence, binary operation * is both commutative and associative.