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
(d) Compute (ca)b and c(ab). 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
(c*a)*b
c*a = a
a*b = c
(c*a)*b = a*b = c
and c(ab)
a*b = c
c*c = d
c*(a*b) = c*c = d
(ca)b not equal c(ab)

2.
it is not asosiative