Question 1084534
<pre>
By Venn diagram:

{{{drawing(300,200,-4,4,-2,4.8, locate(-2,1.8,x),locate(1.5,1.7,z),locate(-3.7,-1,w), locate(-3.6,2.5,A), locate(-.1,1.8,y),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,B)
 )}}}

n(A&#8746;B) = x + y + z = 40, 

n(A&#8745;B) = y = 10 

n(A) = x + y = 15

n(B) = y + z = ?

So the system of equations is:

(eq. 1)              x + y + z = 40
(eq. 2)                  y     = 10
(eq. 3)              x + y     = 15

Subtract (eq. 3) minus (eq. 2)

 (eq. 3)              x + y     =  15
-(eq. 2)                 -y     = -10
----------------------------------------
                      x         =  5

Subtract (eq. 1) minus (eq. 3)

 (eq. 1)              x + y + z =  40

-(eq. 3)             -x - y     = -15
----------------------------------------
                              z =  25

Substitute x = 5 in (eq. 3)

 (eq. 3)              5 + y     =  15  
                          y     =  10

{{{drawing(300,200,-4,4,-2,4.8, locate(-2,1.8,5),locate(1.5,1.7,25), locate(-3.6,2.5,A), locate(-.15,1.8,10),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,B))}}}

n(B) = y + z = 10 + 25 = 35

----------------------------------

By formula

n(A&#8746;B) = n(A) + n(B) - n(A&#8745;B) 
  40   =  15  + n(B) -  10
  40   =   5  + n(B)
  35   =  n(B)

It's easier to use the formula, but you don't learn 
what's going on unless you understand the Venn diagram
method.

Edwin</pre>