Sets-Relations-And-Functions Question 151

Question: Which of the following is correct?

I. $ n(S\cup T) $ is maximum when n $ n(S\cap T) $ is least, II. If $ n(U)=1000,n(S)=720,n(T)=450, $ then least value of $ n(S\cap T)=170. $

Options:

A) Only I is true

B) Only II is true

C) Both I and II are true

D) Both I and II are false

Show Answer

Answer:

Correct Answer: C

Solution:

  • [c]Both the statements are true. II. $ n(S\cup T)=n(S)+n(T)-n(S\cap T) $ $ =720+450-n(S\cap T) $ $ =1170-n(S\cap T) $

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

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