Q + denote the set of all positive rational numbers. If the binary operation ? on Q + is defined as a ? b = a b 2 , then the inverse of 3 is:

Question

$Q^{+}$ denote the set of all positive rational numbers. If the binary operation $\circ$ on $Q^{+}$ is defined as $a \circ b = \frac{a b}{2},$ then the inverse of 3 is:

Smart Achievers · Accepted Answer

(1)

Ans. $\circ$

Explanation:

Let $e$ be the identity element in $Q^{+}$ with respect to binary operation $\circ$ such that,

$a \circ e = a = e \circ a,$ $\forall a \in Q^{+}$

$\frac{a e}{2} = a$ and $\frac{e a}{2} = a$

$e = 2,$ $\forall a \in Q^{+}$

Thus, 2 is the identity element in $Q^{+}$

Let $b \in Q^{+}$ be the inverse of 3, then

$3 \circ b = e = b \circ 3$

$\frac{3 b}{2} = 2$ and $\frac{b (3)}{2} = 2$

$b = \frac{4}{3}$

Thus, $\frac{4}{3}$ is the inverse.

Solution

Q.
$Q^{+}$ denote the set of all positive rational numbers. If the binary operation $\circ$ on $Q^{+}$ is defined as $a \circ b = \frac{a b}{2},$ then the inverse of 3 is:

1 $\frac{4}{3}$

2 $2$

3 $\frac{1}{3}$

4 $\frac{2}{3}$

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Solution

Q. Q+ denote the set of all positive rational numbers. If the binary operation ∘ on Q+ is defined as a∘b=ab2, then the inverse of 3 is:

1 43

2 2

3 13