Question

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

Answer 1

The binary operation is represented by ∗ and is defined by,

{ a,b }×{ a,b }→{ a,b }

This relation shows that binary operation 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 given by number of elements in the set. There are two elements in the given set so, total number of binary operation is 2 4 .

Thus, there are total 16 binary operations on the given set.

Therefore, option (B) is correct.