Sets And Relations Question 2
Question 2 - 2024 (01 Feb Shift 1)
Let $A={1,2,3, \ldots 20}$. Let $R_{1}$ and $R_{2}$ two relation on $A$ such that
$\mathrm{R}_{1}={(\mathrm{a}, \mathrm{b}): \mathrm{b}$ is divisible by $\mathrm{a}}$
$R_{2}={(a, b): a$ is an integral multiple of $b}$.
Then, number of elements in $R_{1}-R_{2}$ is equal
to
Show Answer
Answer (46)
Solution
$n\left(R_{1}\right)=20+10+6+5+4+3+2+2+2$
$+2+\underbrace{1+\ldots+1}_{10 \text { times }}$
$\mathrm{n}\left(\mathrm{R}_{1}\right)=66$
$\mathrm{R}{1} \cap \mathrm{R}{2}={(1,1),(2,2), \ldots(20,20)}$
$\mathrm{n}\left(\mathrm{R}{1} \cap \mathrm{R}{2}\right)=20$
$\mathrm{n}\left(\mathrm{R}{1}-\mathrm{R}{2}\right)=\mathrm{n}\left(\mathrm{R}{1}\right)-\mathrm{n}\left(\mathrm{R}{1} \cap \mathrm{R}_{2}\right)$
$=\mathrm{n}\left(\mathrm{R}_{1}\right)-20$
$=66-20$
$\mathrm{R}{1}-\mathrm{R}{2}=46$ Pair
