Question

Let X={1,2,3,4,5},Y={1,3,5,7,9}.Which of the following is a relation from X to Y?
a. R1={(x,y)y=2+x,x E X,y E Y}
b. R2={(1,1),(2,1),(3,3),(4,3),(5,6)}
c. R3={(1,1),(1,3),(3,5),(3,7),(7,3),(5,7)}
d. R4={(1,3),(2,5),(2,4),(7,9)}
Please answer this question with correct explanation

Answer 1

The correct answer is option (a).$. R_1={[(x,y)y=2+x,x E X,y E Y}]$

Explanation :

• The relation $R_1$ is a relation from X to Y.
• In the other options i.e. in the relations $R_2$ , $R_3$ and $R_4$ we have elements which are not present in either domain or in co - domain.
• Such as in $R_2$ we have the element (5,6) but 6 does not belong to co - domain .
• Similarly in $R_3$ and $R_4$ we have the element 7 in the domain which is wrong .
• But in $R_1$ we can not have the element (2,4)  because 4 does not belong to the set Y and (4,6 ) also .

So, correct answer is $R_1 =$ { (1,3) , (3,5) ,(5,7) }