Define an associative binary operation on a set.

Define a binary operation on a set.

Define a commutative binary operation on a set.

Show that addition and multiplication are associative binary operation on R. But subtraction is not associative on R. Division is not associative on R*.

Let A be a non-empty set and S be the set of all functions from A to itself. Prove that the composition of functions 'o' is a non-commutative binary operation on Sdot Also, prove that 'o' is an associative binary operation on Sdot

Discuss the commutativity and associativity of the binary operation * on R defined by a*b=(a b)/4 for all a ,b in R dot

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

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

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

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

Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod 6). Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of adot OR A binary operation * on the set {0,1,2,3,4,5} is defined as a*b={a+b ,ifa+b<6a+b-6,ifa+bgeq6 Show that zero is the identity for this operation and each element a of set is invertible with 6-a , being the inverse of a.