Assertion (A): A relation R = ( a , b ) : | a - b |<3 defined on … - Vidyadip

MCQ

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 $(a, c) \in R$.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
✓
A is true but R is false.
D
A is false but R is true.

✓

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 $(a, c) \in R$

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