SOLUTION: If n(A)=10,n(A u B) =28 and n(A n B)=6; what is n(B)?

There are three ways to do it:  Venn diagram, chart and formula.
I'll show you all three ways:

Here's how to do it by Venn diagram:



The red circle represents the set A,
The blue circle represents the set B,
The overlapping part represents their intersection 
AnB, or A and B
The left side of the red circle represents A only,
or A and not B, written AnB'
The right side of the blue circle represents B only,
or B and not A, or in alphabetical order, not A and B,
written AnB'

We are given the overlapping part, n(AnB)=6 so we replace
n(AnB) by 6:



Now since we are given that n(A)=10, we know that the other part
of the red circle must contain the other 4, so we replace n(AnB')
by 4:



Finally we are given that AuB=28, which includes both circles,
so since we only have one part to fill, A'nB, we know that it
must be 28-10 = 18.  So we replace A'nB by 18:

 

Answer: n(B) = 6+18 = 24

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Here's how to do it by chart:  n means "and", u means "or",
prime (') after a set means "everything but that set" 

           B          B'     totals      
-------|----------|----------|--------
A      |n(AnB)=6  | n(AnB')  |n(A)=10
-------|----------|----------|--------
A'     |n(A'nB)=? |n(A'nB')=?|n(A')=?  
-------|----------|----------|--------
totals | n(B)=?   | n(B')=?  |  28

We will assume that A'nB' is empty, so we fill in n(A'nB')=0
We fill in n(A')=18 because 28-10 = 18
We fill in n(A'nB)=18 because 18-0 = 18
We fill in n(AnB')=4 because 10-6 = 4


           B          B'     totals      
-------|----------|----------|--------
A      |n(AnB)=6  | n(AnB')=4|n(A)=10
-------|----------|----------|--------
A'     |n(A'nB)=18|n(A'nB')=0|n(A')=18  
-------|----------|----------|--------
totals | n(B)=?   | n(B')=?  |  28

Now we can fill in n(B)=24 because 6+18=24,
which is what we were asked for.  We can
also fill in n(B') both because 4+0=4 and
also because 28-24 = 4. 

           B          B'     totals      
-------|----------|----------|--------
A      |n(AnB)=6  | n(AnB')=4|n(A)=10
-------|----------|----------|--------
A'     |n(A'nB)=18|n(A'nB')=0|n(A')=18  
-------|----------|----------|--------
totals | n(B)=24  | n(B')=4  |  28 

Answer n(B)=24.

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Here's how to do it by formula.  No thinking required.
Just plug in the magic formula, turn the crank, and out
pops the answer. 

If n(A)=10,n(A u B) =28 and n(A n B)=6; what is n(B)?

The magic formula is

n(AuB) = n(A) + n(B) - n(AnB)

   28  =  10  + n(B) -   6
   
    28 = 4 + n(B)

    24 = n(B)

Edwin