Question

How many number of binary operations on the set (A,b)

Answer 1

The number of functions from a set with m elements to a set with n elements is nm.

Binary operation is also a function from a set Sx S  to S.

So, The number of binary operations on the set S  with n elements is (nn)^2

So , the number of binary operations on the set {a,b} with 2 elements is( 22)^2  = 2 4

hope it helps!!!!!

Answer 2

((A,A),(A,b),(b,A),(b,b))-(A,b)is 2^4=16.
so the number of binary operations on the set (A,b)
is 16.