The binary operation `**` on the set `A={1,2,3,4,5}` is defined by `a**b=` maximum of a and b. Construct the composition table of the binary operation `**` on A.

A binary operaiton ^^ on the set A={1,2,3,4,5} is defined by a^^b=min(a,b) for all a,binA. prepare composition table for the operation ^^ on A.

Consider the binary opertion ^^ on the set {1,2,3,4,5} defined by a ^^ b = min {a,b}. Write the opertion table of the opertion ^^.

A binary operation ** is defined on the set S={0,1,2,3,4} as follows: a**b=a+b(mod5) Prove that 0inS is the identity element of the binary operation ** and each element ainS is invertible with 5-ainS being the inverse of the element a.

An operation ** is defined on the set S={1,2,3,5,6} as follows: a**b=ab(mod7) Construct the composition table for operation ** on S and discuss its important properties.

A binary operation ** on QQ , the set of rational numbers, is defined by a**b=(a-b)/(3) fo rall a,binQQ . Show that the binary opearation ** is neither commutative nor associative on QQ .

If ** be the binary operation on the set ZZ of all integers, defined by a**b=a+3b^(2) , find 2**4.

Let be binary operation on the set R defined by a*b = a+b+ab, a, binR . solve equation :2*(2*x)=7

If the binary operation ** on the set ZZ is defined by a**b=a+b-5 , then the identity element with respect to ** is K . Find the value of K .

An operation ** is defined on the set A={1,2,3,4} as follows: a**b,ab(mod5) for all a,binA .Prepare the compositon table for ** on A and from the table show that - (i) multiplication mod(5) is a binary operation, (ii) ** is commutative on A, (iii) is the identity element for multiplication mod(5) on A, and. (iv) every element of A is invertible.

Define a commutative binary operation no a non-empty set A.