Show that `+:RxxRrarrR` and `xx:RxxRrarrR` are commutative binary operations, but `-:RxxRrarrR` and `-::RxxRrarrR` are not commutative.

Show that +: R xx R rarr R and xx : R xx R rarr R are commutative binary operations.

Show that :- R xx RrarrR and div : R xx R rarrR are not commutative binary operations.

Show that *:RxxRrarrR, given by (a,b)rarra+4b^2 is a binary operation.

Show that the binary operation '*' defined from N xx N rarr N and given by a*b = 2a + 3b is not commutative.

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR associative butnot commutative.

Show that subtraction of rational number is not commutative.

Let ∗ be the binary operation on N defined by a*b=H.C.F. of a and b . Is ∗ commutative?

In the binary operation *: Q xx Q rarr Q is defined as : a**b=(ab)/4, a,b inQ Show that * is commutative.

Consider the binary operation: R xx R rarr R defined as : a** b = |a+b| a,b in R . Show that * is commutative.

Consider the binary operations * : RxxRrarrR and o : RxxRrarrR defined as a*b = |a – b| and aob = a, forall a, b in R Show that ∗ is commutative but not associative, o is associative but not commutative. Further, show that ∀ a, b, c in R , a * (b o c) = (a * b) o (a * c) . [If it is so, we say that the operation ∗ distributes over the operation o]. Does o distribute over ∗? Justify your answer.