Let * be a binary operation on `Z` defined by `a*b=a+b-4` for all `a ,\ b in Zdot` Show that * is both commutative and associative.

Let * be a binary operation on Z defined by a*b=a+b-4 for all a,b in Z. show that * is both commutative and associative.

Let * be a binary operation on Q-{-1} defined by a * b=a+b+a b for all a ,\ b in Q-{-1} . Then, Show that * is both commutative and associative on Q-{-1} . (ii) Find the identity element in Q-{-1}

Let * be a binary operation on Q-{-1} defined by a*b=a+b+ab for all a,b in Q-{-1}. Then,Show that * is both commutative and associative on Q-{-1} (ii) Find the identity element in Q-{-1}

Let A be a set having more than one element. Let * be a binary operation on A defined by a*b=a for all a ,\ b in Adot Is * commutative or associative on A ?

Let * be a binary operation on N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

Let ** be binary operation on N defined by a ** b = HCF of a and b. Show that ** is both commutative and associative.

Let * be a binary operation on N defined by a ** b = HCF of a and b. Show that * is both commutative and associative.

** be a binary operation on R defined by a"*"b = (a)/(4)+b/(7) , a,b inR . Show that ** is not commutative and associative.

Let A be a set having more than one element. Let '*' be a binary operation on A defined by a*b=sqrt(a^2 + b^2) for all a , b , in A . Is '*' commutative or associative on A?

On the set Z of integers a binary operation * is defined by a*b= a b+1 for all a ,\ b in Z . Prove that * is not associative on Zdot