| Directions: (1 - 13) |
| The following questions consist of two statements, one labelled as "Assertion [A] and the other labelled as Reason [R]". You are to examine these two statements carefully and decide if Assertion [A] and Reason [R] are individually true and if so, whether the Reason [R] is the correct explanation for the given Assertion [A]. Select your answer from following options. |
| Assertion: A relation R = {(1, 1), (1, 3), (3, 1), (3, 3), (3, 5)} defined on the set \[A=\left\{ 1,3,5 \right\}\]is reflexive. |
| Reason: A relation R on the set A is said to be transitive if for. \[\left( a,\text{ }b \right)~\in R\] and \[\left( b,\text{ }c \right)\in R\], we have \[\left( a,\,c \right)\in R\]. |
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: D
Solution :
Given \[R\text{ }=\text{ }\left\{ \left( 1,1 \right),\left( 1,3 \right),\left( 3,1 \right),\left( 3,3 \right),\left( 3,5 \right) \right\}\] We know that Relation 'R' is reflexive on set A if \[\forall \,a\,\in A,\,\left( a,\,\,a \right)\in \,R\] Here set \[A=\left\{ 1,3,5 \right\}\] \[\left( 1,\,\,1 \right)\in R,\,\left( 3,\,\,3 \right)\in R\]but \[\left( 5,\,5 \right)\notin R\] \[\therefore \]R is not reflexive \[\therefore \]Assertion A is false By definition of transition Relation, It is clear that given Reason R is true. Hence option [D] is the correct answer.
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