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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