Prove that the operation 'addition' on the set of irrational numbers is not a binary operation.

Prove that the operation @ on QQ , the set of rational numbers, defined by a@b=ab+1 is binary operational on QQ .

Number of binary operations

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a+ab . Is the binary operation commutative and associative ?

Let ** be a binary operation on the set Q of rational numbers as follows a**b=(a-b)^2 . Is the binary operation commutative and associative ?

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a^2+b^2 . Is the binary operation commutative and associative ?

The set of netural numbers is closed under the binary operations of :

Define a binary operation on a set.

Define a binary operation on a set.

Define a binary operation on a set