Let $X = \{ 1,\,2,\,3,\,4,\,5\} $ and $Y = \{ 1,\,3,\,5,\,7,\,9\} $. Which of the following is/are relations from $X$ to $Y$

  • A

    ${R_1} = \{ (x,\,y)|y = 2 + x,\,x \in X,\,y \in Y\} $

  • B

    ${R_2} = \{ (1,\,1),\,(2,\,1),\,(3,\,3),\,(4,\,3),\,(5,\,5)\} $

  • C

    ${R_3} = \{ (1,\,1),\,(1,\,3)(3,\,5),\,(3,\,7),\,(5,\,7)\} $

  • D

    both (B) and (C)

Similar Questions

Let $A=\{x, y, z\}$ and $B=\{1,2\} .$ Find the number of relations from $A$ to $B$.

Let $A=\{1,2,3,4,6\} .$ Let $R$ be the relation on $A$ defined by $\{ (a,b):a,b \in A,b$ is exactly divisible by $a\} $

Find the domain of $R$

Let $A=\{1,2,3,4\}, B=\{1,5,9,11,15,16\}$ and $f=\{(1,5),(2,9),(3,1),(4,5),(2,11)\}$
Are the following true?

$f$ is a relation from $A$ to $B$

Justify your answer in each case.

The Fig shows a relationship between the sets $P$ and $Q .$ Write this relation

in set-builder form 

What is its domain and range?

The Fig shows a relation between the sets $P$ and $Q$. Write this relation 

in roster form

What is its domain and range ?