JEE Main 2020MathematicsSets and RelationsMediumMCQ

JEE Main 2020 — Sets and Relations Question with Solution

JEE Main 2020 (03 Sep Shift 2)

Question

Let R1 and R2 be two relations defined as follows :

R1=a, b∈R2:a2+b2∈Q and R2=a, b∈R2:a2+b2∉Q, where Q is the set of all rational numbers, then

Choose an option

Show full solutionCorrect option: C
Correct answer
CNeither R1 nor R2 is transitive.

Step-by-step explanation

For R1 let a=1+2, b=1-2, c=814

aR1b⇒a2+b2=1+22+1-22=6∈Q

bR1c⇒b2+c2=1-22+8142=3∈Q

aR1c⇒a2+c2=1+22+8142=3+42∉Q

∴R1 is not transitive.

For R2 let a=1+2, b=2, c=1-2

aR2b⇒a2+b2=1+22+22=5+22∉Q

bR2c⇒b2+c2=22+1-22=5-22∉Q

aR2c⇒a2+c2=1+22+1-22=6∈Q

∴R2 is not transitive.

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About this question

This is a previous-year question from JEE Main 2020, covering the Sets and Relations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.