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.

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.

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 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 a set A={1,2,3,4} as follows: a*b=ab(mod5), all a,b in A ,Prepare the composition table for '*' on A and from the table show that, '*' is a binary opration and '*' is commutative on A.

Prepare the composition table for multiplication (xx) on the set of fourth roots of unity and discuss its important properties.

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 set A={1,-1,i,-i} of four roots of unity. Constructing the composition table for multiplication on S. which of the properties are true?

A binary operation @ is defined on the set A={0,1,2,3,4,5} as follows: a@b=a+b(mod6) for all a,binA. Prove that oinA is the identity element In A is invertible with operation @ and each element A is invertible with 6-ainA being the inverse of the element a.

The operation ** is defined by a**b=a^(b) on the set Z={0,1,2,3,…} . Show that ** is not a binary operation.

The operation @ is defined by a@b=b^(a) on the set Z={0,1,2,3,…} . Prove that @ is not a binary opeartion on Z.