Question

verify whether the operation* defined onQ by a*b =ab/2 is associative or not​

Answer 1

Step-by-step explanation:

Let a, b, c ∈ Q.

Now, (a*b)*c = (ab/2)*c = (ab/2)c/2 = abc/4

a*(b*c) = a*(bc/2) = a(bc/2)/2 = abc/4

Since (a*b)*c = a*(b*c) the operation * on Q is associative.

Answer 2

Answer:

Since $(a*b)*c=a*(b*c)$, the operation * is associative

Step-by-step explanation:

Let a, b, c ∈ Q

Given that the operation * is defined on Q by $a*b = \frac{ab}{2}$

Consider,

$(a*b)*c=\frac{ab}{2}*c$

               $=\frac{abc}{4}$  → (1)

$a*(b*c)$ $=a*\frac{bc}{2}$

               $=\frac{abc}{4}$  → (2)

From (1) and (2)

$(a*b)*c=a*(b*c)$

Since $(a*b)*c=a*(b*c)$, the operation * defined on Q by $a*b = \frac{ab}{2}$ is associative