in n(a)=20,n(b)=15and n(AuB)=25 then n(AnB)?
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n(A△B)=n(A∪B)−n(A∩B)
for n (A \triangle B)tobemax.n (A \cap B)=0$$
We know, that
n(A∪B)=n(A)+n(B)−n(A∩B)=15+25−0=40
⇒n(A△B)
max
=40−0=40
For minimum value of n(A△B)
n(A∪B) should be min, n(A∩B) should be max.
n(A△B) min =25−15=10
So. value of
n(A△B)=n(A∪B)−n(A∩B) lies om the set
10,11,12,......,3,9,40
Now, when n(A△B) is max. i.e. when
n(A∪B)=40 & n(A∩B)=0
If we decrease n(A∪B) by 1 then n(A∩B)
Will increase by 1
n(A△B)=39−1=38
Similarly on for the decrease of 1 you will get in (A△B) as 36 and 30 so on.
Hence
Range of n(A△B)=10,12,14,16,18,20,......,38,40
=16 values
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