Consider the operations '*' and `o+` on the set R of all real numbers defined as a* b = |a-b| and a `o+` b = a for all a, b `in` R.
Prove that `o+` is associative but n ot commutative.

Consider the operations '*' and o+ on the set R of all real numbers defined as a* b = |a-b| and a o+ b = a for all a, b in R. Prove that '*' is commutative but not associative.

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

Consider the binary operations * : R xx R to R and o: R xx R to R defined as a * b = |a-b| and a o b = a for all a,b in R . Show that '*' is commutative but not associative, 'o' is associative but not commutative.

Let a mapping '*' from Q xx Q to Q (set of all rational numbers) be defined by a* b = a +2 b for all a, b in Q. Prove that the given operation is not 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.

Let A=Set of all real numbes except 1. Let * be defined as a+b-ab for all a, b in A .Show that * is associative

Let a mapping '*' from Q xx Q to Q (set of all rational numbers) be defined by a* b = a +2 b for all a, b in Q. Prove that the given operation is not associative.

Let * : Q xx Q rarr Q be defined a as a * b = 1 + ab for all a, b in Q. Show that * is commutative but not associative.

Let a mapping '*' from Q xx Q to Q (set of all rational numbers) be defined by a* b = a +2 b for all a, b in Q. Prove that * is a binary operation on Q

Let '*' be a binary operation on the set n of natural numbers defined by the rule a* b = a^b for all a , b in N. Is '*' associative?