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Let X = {a,b,c,d} and let be the binary operation on X given by the following table: a b c d a d c a b b c b a c c a a d c d b d c a (c) Compute (ad)c and a(dc). Can you tell, based on this computation, whether is associative? Explain. Solution Let X = {a,b,c,d} and let be the binary operation on X given by the following table: a b c d a d c a b b c b a c c a a d c d b d c a (ad)c a*d = b b*c = a (a*d)*c = b*c = a and a(dc) d*c = c a*c = a a*(d*c) = a*c = a (ad)c = a(dc) = a it is asosiative .

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- 1. Let X = {a,b,c,d} and let be the binary operation on X given by the following table: a b c d a d c a b b c b a c c a a d c d b d c a (c) Compute (ad)c and a(dc). Can you tell, based on this computation, whether is associative? Explain. Solution Let X = {a,b,c,d} and let be the binary operation on X given by the following table: a b c d a d c a b b c b a c c a a d c d b d c a (ad)c a*d = b b*c = a (a*d)*c = b*c = a and a(dc) d*c = c a*c = a a*(d*c) = a*c = a (ad)c = a(dc) = a