Domain and Range of the Relation

Assertion $\left(\mathrm{A}\right)$: Domain and range of a relation $R=\left\{\left(x,y\right):x-3y=0\right\}$ defined on the set $\mathrm{A}=\left\{1,2,3\right\}$ are respectively $\left\{1,2,3\right\} \mathrm{and} \left\{2,4,6\right\}$.

Reason $\left(\mathrm{R}\right)$: Domain and Range of a relation $\mathrm{R}$ are respectively the sets $\left\{a:a\in A \mathrm{and} \left(a,b\right)\in R\right\} \mathrm{and} \left\{b:b\in A \mathrm{and} \left(a,b\right)\in R\right\}$

If $\left(a,b\right)\in R$ such that $a^2+1=b$ where relation $R$ is subset of $A\times B,$ then the number of elements in range of relation $R$ $\left(\text{where} A=\left\{-1,0,1,2\right\} \text{and} B=\left\{1,2,3\right\}\right)$.

If $(a,b)\in R$ such that $a^2+1=b$ where relation $R$ is subset of $A\times B$, then number of elements in range of relation $R$ (where$A=\{-1,0,1,2\}\text{ and }B=\{1,2,3\}$.

Let $R=\left\{\right(x,y);x+2y<6, x,y\in N\}$. Find the range of $R$.

For the function $h\left(x\right)={10}^{1+x}$ the domain of real values of $x$ where $0\le x\le 9$, the range is

The range of the function $f\left(x\right)={\log }_{10}(1+x)$ for the domain of real values of $x$ when $0\le x$$\le 9$ is

The function $f\left(x\right)=2^x$ is

Let the domain of $x$ be the set $\left\{1\right\}$. Which of the following functions gives values equal to $1$

The domain and range of $\left\{(x,y):y=x^2\right\}$ where $x,y\in R$ is

The range of $\left\{\right(3,0),(2,0),(1,0),(0,0\left)\right\}$ is

The domain of $\left\{\right(1,7),(2,6\left)\right\}$ is

A relation $R$ is defined in the set $Z$ of integers as follows $\left(x, y\right)\in R$ if and only if $x^2+y^2=9$. Which of the following is false?

If a relation $R$ defined on the set of integers $I$ such that $R=\left\{\left(x,y\right):2x^2+3y^2\le 15, x,y\in I\right\}$, then the range of $R^{-1}$ is

Let $R=\left\{\left(x,y\right):x+2y=8\right\}$  be a relation on $\mathrm{N}$. Range of $R$ is given as $\left\{a,b,c\right\}$ where $a,b,c$ are the elements of the range and $a>b>c$. Find the number $abc$.

If $R=\left\{(x,y):x^2+y^2\le 4, x,y\in \mathrm{Z}\right)$ is a relation on $\mathrm{Z} \left(\mathrm{Z} \mathrm{represents} \mathrm{an} \mathrm{integer}\right)$, then domain of $R$ is

Let $f$ be a real valued function defined as $f\left(x\right)=\frac{\sqrt{x-4\sqrt{x-4}} \cdot x}{\sqrt{x-4}-2}$,which of the following statement holds true regarding $f$

If $A=\left\{1,2,3\right\},\mathrm{ }B=\left\{1,4,6,9\right\}$ and $R$ is a relation from $A$ to $B$ defined by $\mathrm{‘}x$ is greater than $y\text{'}$ . The range of $R$ is

If $R=\left\{\left(x,\mathrm{ }y\right)|x,\mathrm{ }y\in Z,\mathrm{ }{x}^2+y^2\le 4\right\}$ is a relation in $Z$ , then domain of $R$ is

Let $R$ be a relation on $N$ defined by $x+2y=8$ . The domain of $R$ is

A relation $R$ is defined from $\left\{2,\mathrm{ }3,\mathrm{ }4,\mathrm{ }5\right\}$ to $\left\{3,\mathrm{ }6,\mathrm{ }7,\mathrm{ }10\right\}$ by $xRy\iff x$ is relatively prime to $y$ . Then domain of $R$ is