Distributivity of binary operations

Associativity of binary operations

Commutativity of binary operations

Discuss the commutativity and associativity of binary operation* defined on Q by the rule a*b=a-b+ab for all a,b in Q

Number of binary operations

Let * be the binary operation on N defined by aquad *,b commutative? Is * associative? Does there exist identity for this binary operation on N ?

Let * be the binary operation on N defined by a*b=HCF of a and b .Does there exist identity for this binary operation on N?

Which of the following is true? * defined by a*b=(a+b)/2 is a binary operation on Z (b) * defined by a*b=(a+b)/2 is a binary operation on Q (c) all binary commutative operations are associative (d) subtraction is a binary operation on N

Let A = {1, 2, 3}. Find the number of binary operations on A.

On Z an operation * is defined by a*b=a^(2)+b^(2) for all a,b in Z .The operation* on Z is commutative and associative associative but not commutative (c) not associative (d) not a binary operation