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# Let X - {a-b-c-d} and let be the binary operation on X given by the f.docx

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# Let X - {a-b-c-d} and let be the binary operation on X given by the f.docx

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
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
it is asosiative
.

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
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