R S Aggarwal Solutions for Exercise 3: OBJECTIVE QUESTIONS

Let $A$ be the set of all points in a plane and let $O$ be the origin. Let $R=\left\{\left(P,Q\right): OP=OQ\right\}$. Then, $R$ is

Let $Q$ be the set of all rational numbers and $*$ be the binary operation, defined by $a*b=a+2b$, then

Let $a* b=a+ab$for all $a, b\in Q$. Then,

Let $Q^{+}$ be the set of all positive rationals. Then, the operation $*$ on is $Q^{+}$ defined by $a*b=\frac{ab}{2}$ for all $a, b\in Q^{+}$ is

Let $Z$ be the set of all integers and let $a*b=a-b+ab$. Then,$*$ is

Let $Z$ be the set of all integers. Then, the operation $*$ on $Z$ defined by $a*b=a+b-ab$ is

Let $Z^{+}$ be the set of all positive integers. Then the operation $*$ on $Z^{+}$ defined by $a*b=a^b$ is

Define $*$ on $Q-\left\{-1\right\}$ by $a*b=a+b+ab$. Then, $*$ on $Q-\left\{-1\right\}$ is