Introduction to Relation

Q.

Describe difference between relation and function.

Q.

Write a function rule for “the output is twice the input”.

Q.

What is the initial value of the function represent by this table ?

$x$	$y$
$0$	$3$
$1$	$5$
$2$	$7$

1. $0$

2. $2$

3. $3$

4. $5$

Q. A relation is a collection of ordered pairs $(x,y)$.

1. True
2. False

Q. Which of following options is the correct representation of relation from set A to set B?
$A=\{1,2,3,4\}\&B=\{1,2,3,5\}R=\left\{\right(x,y):x\in A,y\in B\&x=y\}$

1. $\left\{\right(1,1),(2,2),(3,3)$
2. $\left\{\right(1,2),(2,3),(3,4)$
3. $\left\{\right(1,1),(2,2),(3,3),(4,4)$

Q. The relation from one set to other is defined as the collection of ordered pair, in which each ordered pair consists relating elements of both sets.

1. True
2. False

Q. A relation $R$ is defined as $R=\left\{\right(x,y):x<y\}$. Which among the following options is an ordered pair of $R$?

1. $(24,24)$
2. $(65,40)$
3. $(45,54)$

Q. A mother and her child are not connected by any relation.

1. True
2. False

Q. Determine whether the following relation in the table from set $X$ to set $Y$ describes a function or not.
$X:\{-3,4,2,-1\}Y:\{0,4,7,10\}$

Input (x)	Output (y)
-3	0
-1	4
2	7
4	10

Here $x\in X\&y\in Y$

1. It represent a function
2. Does not represent function

Q. Which of the following statement(s) is/are correct?

1. Set of first element of all ordered pairs of a relation is called domain.
2. Set of first element of all ordered pairs of a relation is called range.
3. Set of second element of all ordered pairs of a relation is called range.
4. Set of second element of all ordered pairs of a relation is called domain.