Let S be a set of two elements. How many different binary operaions can be defined on S?

Let A be a set of 3 elements. The number of differentity binary operations can be defined A is…

Let S be any set containing more than two elements. A binary operation @ is defined on S by a@b=b for all a,binS . Discuss the commutativity and associativity of @ on S.

Let S be a set of containing more than two elements and a binary operaton @ on S be defined by a@b=a for all a,binS . Prove that @ is associative but not commutative on .

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?

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?

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

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 A and B be two sets containing respectively m and n distinct elements. Then number of different relations can be defined from set A to set B is ___

Let S be a set containing n elements.Then the total number of binary operations on S is

Let R be the set of real numbers and * be the binary operation defined on R as a*b= a+ b-ab AA a, b in R .Then, the identity element with respect to the binary operation * is