Question

Number of binary operations on the set {a, b} are
(A) 10
(B) 16
(C) 20
(D ) 8

Answer 1

binary operation * on {a, b} is a function from {a, b} × {a, b} → {a, b}

i.e., * is a function from {(a, a), (a, b), (b, a), (b, b)} → {a, b}.

The total number of binary operations on the set {a, b} is 24 i.e., 16.

therefore, correct option is b

Answer 2

No. of elements in set = 2
So, total no. of binary operations on this set
=(2)^(2*2)
=(2)^(4)
=16