Let - be a binary operation on Q- defined by a- b - ab2- - a- b- Q-Determine whether - is associative or not-

Given: a∗ b = ab2, ∀ a, b∈ Q then ∀ a, b, cϵ Q we have a∗ (b∗ c) = a∗ (bc2 ) = a (bc2 )2 = abc4 and (a∗ b)∗ c = ab2∗ c = (ab2 )c2 = abc4 ...

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Associative Law of Binary Operation

Let ∗ be a ...

Question

Let $$ be a binary operation on $Q$ , defined by $a b = \frac{a b}{2}, \forall a, b \in Q$ .
Determine whether $*$ is associative or not.

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For given binary operation $*$ defined below, determine whether $*$ is binary, commutative or associative.
(iii)On Q, define $a * b = \frac{a b}{2}$

For given binary operation $*$ defined below, determine whether $*$ is binary, commutative or associative.
(ii)On Q, define $a * b = a b + 1$

*

a * b = 2^{a b}

For each binary operation $*$ defined below, determine whether $*$ is binary, commutative or associative.
(i) On Z, define a $*$ b =a-b

(ii) On Q, define $a * b = a b + 1$

(iii) On Q, define $a * b = \frac{a b}{2}$

(iv) On $Z^{+}$ , define $a * b = 2^{a b}$

(v) On $Z^{+}$ , define $a * b = a^{b}$

(vi) On (R-{-1} ,define $a * b = \frac{a}{b + 1}$

A = Q \times Q

(a, b) * (c, d) = (a c, b + a d) f o r (a, b), (c, d) ϵ A .

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