First slide

Introduction to Relations (XI) on Sets

Question

Let A be the set of first ten natural numbers and let R be a relation in A defined by if and only if x+2y=10 Which of the following is false?

Easy

A

R={(2,4),(4,3),(6,2),(8,1)}
B

Domain of R={2,4,6,8}
C

Range of R={1,2,3,4}
D

Atleast one is false

Solution

We have,
R={(x,y):x,y $\in$ N,x+2y=10,1 $\leq$ x,y $\leq$ 10}
x+2y=10
$\Rightarrow$ y= $\frac{10 - x}{2}$
R={(2,4),(4,3),(6,2)(8,1)}
Domain of R={x:(x,y) $\in$ R={2,4,6,8}
Range of R={y:(x,y) $\in$ R}={4,3,2,1}

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