Question

n(A)=1000,n(B)=500 if n(A union B)=p and n(A intersection B)>=1 then p lies b/w in

Answer 1

p lies in interval

p ∈ [1000, 1499]

Step-by-step explanation:

Given

$n(A)=1000$

$n(B)=500$

$n(A\cup B)=p$

$n(A\cap B)\ge 1$

To find out

The interval in which p lies

Solution

We know that

For sets A and B

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

$\implies p=1000+500-n(A\cap B)$

$\implies n(A\cap B)=1500-p$

$n(A\cap B)\ge 1$

$\implies 1500-p\ge 1$

$\implies 1500\ge 1+p$

$\implies p\le 1500-1$

$\implies p\le 1499$

Also, the maximum value of $n(A\cap B)$ can be 500 in which case B will be subset of A

Thus,

$n(A\cap B)\le 500$

$\implies 1500-p\le 500$

$\implies 1500-500\le p$

$\implies p\ge 1000$

Thus,

$1000\le p\le 1499$

$\implies p\in [1000, 1499]$

Hope this answer is helpful.

Know More:

Q: If a b and c are three sets and U is the universal set such that n(U)=700 ,n(a)=200, n(b)=300 and find n(a intersection b) =100. Find n(a compliment intersection b compliment)

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