| 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 \[n(S\cap T)=170.\] |
A) Only I is true
B) Only II is true
C) Both I and II are true
D) Both I and II are false
Correct Answer: C
Solution :
[c]Both the statements are true. II. \[n(S\cup T)=n(S)+n(T)-n(S\cap T)\] \[=720+450-n(S\cap T)\] \[=1170-n(S\cap T)\] \[\Rightarrow 1170-n(S\cap T)\le n(U)\Rightarrow 1170-n(S\cap T)\le 1000\]\[\Rightarrow n(S\cap T)\ge 170\]
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