MCQ 11 Mark
Assertion (A): A relation $R =\{( a , b )$ : $| a - b |<3\}$ defined on the set $A =\{1,2,3,4\}$ is reflexive.
Reason (R): A relation $R$ on the set $A$ is said to be reflexive if for $(a, b) \in R$ and $(b, c) \in R$, we have $(a, c) \in R$.
Reason (R): A relation $R$ on the set $A$ is said to be reflexive if for $(a, b) \in R$ and $(b, c) \in R$, we have $(a, c) \in R$.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- ✓A is true but R is false.
- DA is false but R is true.
Answer
View full question & answer→Correct option: C.
A is true but R is false.
(c) A is true but R is false.
Explanation: Assertion is true because for each element $a \in A ,| a - a |=0<3$, so $(1,1) \in R,(2,2) \in R,(3,3) \in R,(4,4)$ $\in R$ therefore R is reflexive.
Reason is false because a relation $R$ on the set $A$ is said to be transitive if for $(a, b) \in R$ and $(b, c) \in R$, we have $(a, c) \in R$
Explanation: Assertion is true because for each element $a \in A ,| a - a |=0<3$, so $(1,1) \in R,(2,2) \in R,(3,3) \in R,(4,4)$ $\in R$ therefore R is reflexive.
Reason is false because a relation $R$ on the set $A$ is said to be transitive if for $(a, b) \in R$ and $(b, c) \in R$, we have $(a, c) \in R$