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
$R _1=(a, b): b$ 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
Show Answer
Answer (46)
Solution
$n\left(R _1\right)=20+10+6+5+4+3+2+2+2$
$+2+\underbrace{1+\ldots+1} _{10 \text { times }}$
$n\left(R _1\right)=66$
$R _1 \cap R _2={(1,1),(2,2), \ldots(20,20)}$
$n\left(R _1 \cap R _2\right)=20$
$n\left(R _1-R _2\right)=n\left(R _1\right)-n\left(R _1 \cap R _2\right)$
$=n\left(R _1\right)-20$
$=66-20$
$R _1-R _2=46$ Pair
