| Assertion: A relation \[R=\left\{ \left( x,\,y \right)\,\,:\,\,|\,x\,-\,y|\,=0 \right\}\] defined on the set A = {3, 5, 7} is symmetric. |
| Reason: A relation R on the set A is said to be symmetric if for \[\left( a,\,\,b \right)\in R\], we have \[\left( b,\,\,a \right)\in R\]. |
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: A
Solution :
Given \[R=\left\{ \left( x,\,y \right)\,:\,\left| x-y \right|=0 \right\}\] \[=\text{ }\left\{ \left( 3,\text{ }3 \right),\text{ }\left( 5,\text{ }5 \right),\text{ }\left( 7,\text{ }7 \right) \right\}\] We know that A relation R is symmetric if \[\left( a,\,\,b \right)\,\,\in R\]and \[\left( b,\,\,a \right)\,\,\in R\,\,\forall \,\,a,\,\,b\in \,\,A\,\] Here \[\] \[\therefore \]R is symmetric \[\Rightarrow \]Assertion [A] is true. Also given Reason R is true (Definition of symmetric relation) and is correct explanation of A. Hence option [A] is the correct answer.
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