<PRE><B>Question 1119159</B>
.
In a survey of 100 students, the numbers taking various courses were found to be 
English, 59; mathematics, 44; chemistry, 48; English and mathematics, 24; English and chemistry, 26; mathematics and chemistry, 31; 
and courses in all three areas, 16.


&lt;pre&gt;
(a)  How many students were taking mathematics, but neither English nor chemistry?

     M - EM - MC + EMC = 44 - 24 - 31 + 16 = 5.



(b)  How many were taking mathematics and chemistry, but not English?

     MC - EMC = 31 - 16 = 15.



(c)  How many were taking English and chemistry, but not mathematics?

     EC - EMC = 26 - 16 = 10.
&lt;/pre&gt;

Solved.


-------------


In this solution, two-letter abbreviation means intersection of two sub-sets.



</PRE>