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Which of the following is not correct for relation R on... | Relation (Mathematics) | DivineJEE

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Mathematics

JEE Mains ($31^{st\ }$ Aug $1^{st\ }$ Shift 2021) 31st August Shift 1

Mathematics

Which of the following is not correct for relation

R

on the set of real numbers?

A

(x,y) \in R \Leftrightarrow |x| - |y| \leq 1

is reflexive but not symmetric.\\

B

(x,y) \in R \Leftrightarrow |x - y| \leq 1

is reflexive and symmetric.\\

C

(x,y) \in R \Leftrightarrow 0 < |x - y| \leq 1

is symmetric and transitive.\\

D

(x,y) \in R \Leftrightarrow 0 < |x| - |y| \leq 1

is neither transitive nor symmetric.

Correct Answer:

C

Explanation

(c) :

0 < |x - y| \leq 1

is symmetric as

|x - y| = |y - x|

but not transitive.\\ For example :

(1,2),(2,1) \in R

but

(1,1) \notin R

.

Select an option to instantly check whether it is correct or wrong.

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