Show that the number of binary operations on {1, 2} having 1 as identity and having 2 as the inverse of 2 is exactly one.

Number of binary operations on the set {2, 3} ls :

Show that -a is not the inverse of a in N for the addition operation '+' on N and 1/a is not the inverse of a in N for multiplication operation ‘xx’ on N , for a ne 1 .

Write down the number of commutaive binary operations that can be defined on the set (1,2).

Show that the binary operation on the set 'N' given by a * b =1 AA a,b in N is commutative as well as associative.

Show that – a is the inverse of a for the addition operation '+' on R and 1/a is the inverse of a ne 0 for the multiplication operation ‘xx’ on R.

Show that addition, subtraction and multiplication are binary operations on R, but division is not a binary operation on R. Further, show that division is a binary operation on the set R of nonzero real numbers.

Show that the binary operation '*' defined from N xx N rarr N and given by a*b = 2a + 3b is not commutative.

let '*' be a binary operation on R defined by a*b = a+b + ab, where a, b inR , then the value of 1*(2*3) is