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Question

Which of the following is correct?

1. n(ST) is maximum when n(ST) is least.

2. If n(U)=1000,n(S)=720,n(T)=450, then the least value of n(ST)=170.


A

Only 1 is true

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B

Only 2 is true

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C

Both 1 and 2 are true

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D

Both 1 and 2 are false

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Solution

The correct option is C

Both 1 and 2 are true


Explanation for correct option

Using Union Formula,

n(ST)=n(S)+n(T)n(ST)

If the intersection of two sets is minimum i.e., n(ST) then union of set is maximum (ST).

Hence, statement 1 is true.

Given: n(U)=1000,n(S)=720,n(T)=450, Find n(ST)

n(ST)=n(S)+n(T)n(SUT)n(ST)=720+450-1000n(ST)=170

Hence statement 2 is also true.
Hence the correct option is option (c).


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