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.

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.

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 * : 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.

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

Let a mapping '*' from R xx R to R be defined by a * b = 2 a + 2 b for all a , b in Z. Prove that the givne operation is commutative but not associative.

The binary operation ** : R xx R rarrR is defined as a ** b = 2a + b . Find (2** 3) **4

In the binary operation *: Q xx Q rarr Q is defined as : a*b = a + b - ab, a,b in Q Show that * is commutative .