if n(a)=24.......If n(A)=10

Question

a. if n(a)=24

n(b)=10

n(aUb)=28

what do you think about n(A n B)8

b. If n(A)=10

n(B)=18

n(A∪B)=2

what do you think about n(a U b)

Answer 1

Selena, here’s a way to approach this:

the elements of a are either in b or not in b.

Similarly, the elements of b are either in a or not in a.

so Let ainb be the a elements that are also in b,

Let aalone be the a elements that are not in b

Let bina be the b elements that are also in a.

Let balone be the b elements that are not in a.

Now translate what we know into math.

First, notice that ainb = bina

24 = ainb + aalone

10 = bina + balone = ainb + balone

28 = aalone + balone + ainb

From the last two, subtract and find

18 = aalone

from that and the first line, we see that

6 = ainb

and that’s the answer to the question.

So, for the second question, do the same thing: put a name on each quantity, then translate the numbers you know into expressions. Then you can find

aalone + balone + ainb

If you have any questions, please ask.