Show that * on R –{ - 1}, defined by is neither commutative nor associative.

Let Q be the set of all positive rational numbers.

(i) Show that the operation * on Q ⁺ defined by is a binary operation.

(ii) Show that * is commutative.

(iii) Show that * is not associative.

Show that the set A = { - 1, 0, 1) is not closed for addition.

For all a, b ∈ R, we define a * b = |a – b|.

Show that * is commutative but not associative.

For all a, b ∈ N, we define a * b = a³ + b³.

Show that * is commutative but not associative.