| Assertion: Domain and Range of a relation |
| \[R=\left\{ \left( x,\text{ }y \right):x-2y=0 \right\}\]defined on the set \[A=\left\{ 1,2,3,4 \right\}\]are respectively \[\left\{ 1,2,3,4 \right\}\]and\[\left\{ 2,4,6,8 \right\}\]. |
| Reason: Domain and Range of a relation R are respectively the sets \[\left\{ a\,\,\,:\,\,a\,\,\in A \right.\]and \[\left. \left( a,\,\,b \right)\,\,\in \,\,R \right\}\]and \[\left\{ b\,\,:\,\,b\,\,\in \,\,A\,and\,\,\left( a,\,\,b \right)\,\in \,R \right\}\] |
A) Both A and R are individually true and R is the correct explanation of A.
B) Both A and R are individually true and R is not the correct explanation of A.
C) 'A' is true but 'R' is false
D) 'A' is false but 'R' is true
E) Both A and R are false.
Correct Answer: D
Solution :
Given \[R=\left\{ \left( x,\,\,y \right)\,\,:\,\,x-2y=0\,or\,y=\frac{x}{2} \right\}\] \[\therefore \]Range \[=\left\{ \frac{1}{2}\,\,\frac{3}{2} \right\}\] \[\therefore \]Given Assertion is false Also given reason [R] is true {By definition of Domain and Range of Relation} Hence option [D] is the correct answer.
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