Let * be a binary operation on the set Q of r | vedclass

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(C) On the set $Q$,the operation $*$ is defined as $a * b = \frac{ab}{4}$.For commutativity,consider $a, b \in Q$:$a * b = \frac{ab}{4} = \frac{ba}{4}

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The operation is both commutative and associative.

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(C) On the set $Q$,the operation $*$ is defined as $a * b = \frac{ab}{4}$.For commutativity,consider $a, b \in Q$:$a * b = \frac{ab}{4} = \frac{ba}{4} = b * a$.Since $a * b = b * a$,the operation is commutative.For associativity,consider $a, b, c \in Q$:$(a * b) * c = (\frac{ab}{4}) * c = \frac{(\frac{ab}{4})c}{4} = \frac{abc}{16}$.$a * (b * c) = a * (\frac{bc}{4}) = \frac{a(\frac{bc}{4})}{4} = \frac{abc}{16}$.Since $(a * b) * c = a * (b * c)$,the operation is associative.Thus,the operation is both commutative and associative.

Let $$ be a binary operation on the set $Q$ of rational numbers defined as $a b = \frac{ab}{4}$. Which of the following is true?

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Let $*$ be a binary operation on the set $Q$ of rational numbers defined as $a * b = \frac{ab}{4}$. Which of the following is true?

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Let $A = N \times N$ and $^*$ be the binary operation on $A$ defined by $(a, b) \,^*\, (c, d) = (a + c, b + d)$. Determine whether the operation $^*$ is commutative,associative,and has an identity element.

Let $^*$ be the binary operation on $N$ given by $a \,^* \,b = \text{L.C.M. of } a \text{ and } b$. Find $5 \,^* \,7$ and $20 \,^* \,16$.

Let $*$ be a binary operation defined on $R$ by $a * b = \frac{a+b}{4}$ for all $a, b \in R$. Then the operation $*$ is:

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