Question 1117906
.
<pre>
You are given a "universal" set A of 75 cars, and two subsets A of 10 cars and B of 18 cars.


You also are given that the complement to the union of the sets A and B has 53 elements; hence, the union of A and B has  75 - 53 = 22 elements.


Thus we know that  n(AUB) = 23  (the number of elements in the union),  and  n(A) = 10,  n(B) = 18.


Then the number of elements in the intersection  n(AnB) = n(A) + n(B) - n(AUB) = 10 + 18 - 23 = 5.


<U>Answer</U>.  5 cars needed both brake and exhaust system repairs.
</pre>

==============


To get more acquaintance with this circle of problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>

in this site.