Q, the set of all rational number, * is defined by `a * b=(a-b)/2` , show that * is no associative.

Q, the set of all rational number, * is defined by a*b= (a-b)/2 , show that * is not associative.

On Q , the set of all rational numbers a binary operation * is defined by a*b= (a+b)/2 . Show that * is not associative on Qdot

On the set Q of all rational numbers an operation * is defined by a*b = 1 + ab . Show that * is a binary operation on Q.

On Q, the set of all rational numbers, a binary operation * is defined by a*b=(a b)/5 for all a , b in Qdot Find the identity element for * in Q. Also, prove that every non-zero element of Q is invertible.

On Q, the set of all rational numbers, a binary operation * is defined by a*b=(a b)/5 for all a , b in Qdot Find the identity element for * in Q. Also, prove that every non-zero element of Q is invertible.

On the set Q of all rational numbers if a binary operation * is defined by a*b= (a b)/5 , prove that * is associative on Qdot

Let *, be a binary operation on N, the set of natural numbers defined by a * b = a^b , for all a,b in N . Is * associative or commutative on N?

Let * be a binary operation on the set Q_0 of all non-zero rational numbers defined by a*b= (a b)/2 , for all a ,\ b in Q_0 . Show that (i) * is both commutative and associative (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

Let *, be a binary operation on N, the set of natural numbers defined by a*b = a^b , for all a,b in N . is * associative or commutative on N?

On Z , the set of all integers, a binary operation * is defined by a*b= a+3b-4 . Prove that * is neither commutative nor associative on Zdot