Show that addition, subtraction and multiplication are binary operations on R but division is not a binary operation on R.

Show that addition and multiplication are associative binary operations on R.

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

Show that subtraction and division are not associative binary operations on R.

Show that addition and multiplication are associative binary operation on R. But subtraction is not associative on R. Division is not associative on R_∗ .

Number of binary operations on theset (a,b) is

Number of binary operations on the set {a, b} is

Number of binary operations on the set {a, b} is :

Determine whether or not each of the definition of * given below gives a binary operation. In the event that * is not a binary operation, given justification for this. On Z^+ , define * by a * b = a