Question

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

• A. $\left\{\right(1,1),(2,2),(3,3)$
• B. $\left\{\right(1,2),(2,3),(3,4)$
• C. $\left\{\right(1,1),(2,2),(3,3),(4,4)$

Answer 1

The correct option is A $\left\{\right(1,1),(2,2),(3,3)$

Given: The Relation from set A to set B is represented by Relation R.

Relation R represent a straight line $y=x$ where $x\in A$ and $y\in B$.

Given: $A=\{1,2,3,4\}\&B=\{1,2,3,5\}$

1. For $x=1$ we get $y=1$
2. For $x=2$ we get $y=2$
3. For $x=3$ we get $y=3$
4. For $x=4$ we get $y=4$ $\Rightarrow 4\ne 5$

The last value from set A does not map with last value of set B
So, the ordered pair we get are $(1,1),(2,2),(3,3)$.

Collection of ordered pairs is a relation.
Here $R:\left\{\right(1,1),(2,2),(3,3\left)\right\}$