| Assertion: The relation R in set A of human beings in a town at a particular time given by : |
| R = {(x, y) : x is exactly 5 years younger than y} is symmetric. |
| Reason: A relation R on the set A is said to be symmetric if \[\left( a,\,\,b \right)\in R\] but \[\left( b,\,\,a \right)\notin R\]. |
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: E
Solution :
Given R = {(x, y) : x is exactly 5 years younger many} \[\therefore \,\,\,\,\,\,\,\,\,\,y=x+5\] Clearly if \[\left( a,\,\,b \right)\,\,\in \,\,R\]than \[\left( b,\,\,a \right)\notin R\] \[\Rightarrow \]R is not symmetric relation \[\therefore \] Assertion [A] is false Also given Reason is false {By Difinition of symmetric} \[\therefore \]Both A and R are false. Hence option [E] is the correct answer.
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