Is '*' defined on the set {1, 2, 3, 4, 5} by : a * b = L.C.M.. of a and b, a binary operation ? Justify your answer.

Is '*' defined on the set {1,2,3,4,5} by a*b = L.C.M. of a and b a binary operation ? Justif your answer.

Let * be the binary operation on the set {1,2,3,4,5}, defined by a *' b = H.C.F of a and b. Is the operation *' same as the operation * defined above? Justify your answer.

Let a ** b= 2a + b be a binary operation then find 3**4 .

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

Let a binary operation '*' be defined on I (set of integers) by : a * b = 2a + 2b for a, b in I. Prove that given operation is commutative but not associative.

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

Let * be the binary operation on N given by a * b = L.C.M. of a and b. Find. Is * commutative?