Let A=\ 1,2,3, ldots 20\ . Let R 1 and R 2 two relation on A such that R 1 =\ (a, b): b is divisible by a\ R 2 =\ ( a , b ): a is an integral multiple of b \ . Then, number of elements in R 1 -R 2 is equal to .

Mathematics · Sets and Relations

JEE Main 2024 — 1 February, Shift 1 — Question 30

Let $A=\{1,2,3, \ldots 20\}$ . Let $R_{1}$ and $R_{2}$ two relation on A such that $\mathrm{R}_{1}=\{(a, b): b$ is divisible by $a\}$ $\mathrm{R}_{2}=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}$ is an integral multiple of b $\}$ . Then, number of elements in $R_{1}-R_{2}$ is equal to $\qquad$ .

Answer: 46

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{n}\left(\mathrm{R}_{1}\right)=20+10+6+5+4+3+2+2+2$

$+2+\underbrace{1+\ldots+1}_{10 \text { times }}$ $\mathrm{R}_{1} \cap \mathrm{R}_{2}=\{(1,1),(2,2), \ldots(20,20)\}$

$\mathrm{n}\left(\mathrm{R}_{1} \cap \mathrm{R}_{2}\right)=20$

$\mathrm{n}\left(\mathrm{R}_{1}-\mathrm{R}_{2}\right)=\mathrm{n}\left(\mathrm{R}_{1}\right)-\mathrm{n}\left(\mathrm{R}_{1} \cap \mathrm{R}_{2}\right)$

$=\mathrm{n}\left(\mathrm{R}_{1}\right)-20$

$=66-20$

$\mathrm{R}_{1}-\mathrm{R}_{2}=46$ Pair

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 1 February, Shift 1
Subject: Mathematics
Chapter: Sets and Relations
Topic: Relations