Show that subtraction and division are not binary operations on N.

Number of binary operations

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.

Define a binary operation on a set.

Show that addition and multiplication are associative binary operation on R.But subtraction is not asociative on R.Division is not associative on R^(*).

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.

Associativity of binary operations

Distributivity of binary operations

Commutativity of binary operations

Define a commutative binary operation on a set.

Which of the following is true? * defined by a*b=(a+b)/2 is a binary operation on Z (b) * defined by a*b=(a+b)/2 is a binary operation on Q (c) all binary commutative operations are associative (d) subtraction is a binary operation on N