| Assertion: A relation R = {(1, 1), (1, 2), (2, 2), (2, 3), (3, 3)} defined on the set A = {1, 2, 3} is reflexive. |
| Reason: A relation R on the set A is said to be reflexive if \[\left( a,\,a \right)\in R\,\,for all \,\,a\,\,\in \,\,A\]. |
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 \[R\text{ }=\text{ }\left\{ \left( 1,1 \right),\left( 1,\,2 \right),\left( 2,2 \right),\left( 2,3 \right),\left( 3,3 \right) \right\}\] Since \[\left( 1,\,\,1 \right)\in \,R,\,\left( 2,\,\,2 \right)\,\,\in R\]and \[\left( 3,\,\,3 \right)\in \,R\] \[\therefore \]R is reflexive \[\Rightarrow \]Assertion [A] is true. Also given Reason [R] is true {By definition of Reflexive Relations} and is correct explanation of A Hence option [A] is the correct answer.
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