Question

Assertion :Let $n\left(U\right)=1000,n\left(S\right)=720,n\left(T\right)=450$,then least value of $n(S\cap T)$ is $170$ Reason: $n(S\cup T)$ is max. when $n(S\cap T)$ is least

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$n(S\cup T)=n\left(S\right)+n\left(T\right)-n(S\cap T)$

$=720+450-n(S\cap T)$

$n(S\cup T)=1170-n(S\cap T)$

$n(S\cup T)=1170-n(S\cap T)\le n\left(U\right)(\therefore S\cup T\subset U)$

$\therefore 1170-n(S\cap T)\le 1000$

$\Rightarrow n(S\cap T)\ge 170$

$\therefore$ Least value of $n(S\cap T)=170$