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

2.
it is asosiative