Question

how can I answer to this 2 1)-n(a∩b∩c) 2-n(b∩c) n(a)=18 n(b)=21 n(c)=14 n(a∩b)=9 n(a∩c)=9

Answer 1

Answer:

Just take pencil and paper, draw your two sets A and B (making sure they intersect) and write down what you know about them into that drawing!

You’ll see that e.g. the “71” is better written as the sum of two parts, so your drawing will have those two partial cardinalities instead of 71.

The rest of the story should then be peanuts!

Answer 2

Answer:

Ifn(A)=7,n(A∪B)=11,andn(B)=5,thenwhatisn(A∩B)?

Solution

n(A)=7

n(B)=5

n(A∪B)=11

(A∩B)=?

Let the intersection of A and B =n,n(Aonly)=7−n,n(Bonly)=5−n

n(AUB)=n(Aonly)+n(Bonly)+n(AnB)

After you replace the equations in the formula above,

n(AUB)=n(Aonly)+n(Bonly)+n(AnB)

n(AUB)=7−n+5−n+n

Remember our n(AUB)=11,,

11=7−n+5−n+n

Revise the formula for easy understanding starting from n,so

n+5−n+7−n=11

n−n−n+5+7=11

The first two n (s) cancel out and we remain with one, as shown below

5+7−n=11

But 5+7=12

Therefore,

12−n=11

Here n crosses to become a positive (+n) and 11 crosses to the opposite side to become a negative (-11) as shown below,

12−n=11

12−11=n

but 12−11=1

1=n

n=1

But remember we said let the intersection of A and B =n

son(AnB)=n

Theren(AnB)=1.

So Ifn(A)=7,n(A∪B)=11,andn(B)=5,thenn(A∩B)=1.