2. A survey on subjects being taken by 250 college students in Candon City revealed the following information. Subject Number of students taking the subject Mathematics 145 Filipino 90 English 88 Math and Filipino 25 Filipino and English 38 Math and English 59 Math, Filipino and English 15 How many did not take any of the three subjects? How many took Math as their only subject? English only? Filipino only? How many were taking Math and Filipino but not English? How many were taking Filipino and English but not Math?

$N(M\cup F\cup E)=N(M)+N(F)+N(E)$

$-N(M\cap F)-N(M\cap E)-N(F\cap E)$

$+N(M\cap F\cap E)=145+90+88$

$-25-38-59+15=216$

a)

$N(not\ any)=N(U)-N(M\cup F\cup E)$

$=250-216=34$

b)

$N(only\ one)=N(only\ M)$

$+N(only\ F)+N(only\ E)$

$N(only\ M)=N(M)-N(M\cap F)-N(M\cap E)$

$+N(M\cap F\cap E)=145-25-59+15=76$

$N(only\ F)=N(F)-N(M\cap F)-N(F\cap E)$

$+N(M\cap F\cap E)=90-25-38+15=42$

$N(only\ E)=N(E)-N(M\cap E)-N(F\cap E)$

$+N(M\cap F\cap E)=88-38-59+15=6$

$N(only\ one)=76+42+6=124$

c)

$N((M\cap F)-E)=N(M\cap F)-N(M\cap F\cap E)$

$=25-15=10$

d)

$N((F\cap E)-M)=N(F\cap E)-N(M\cap F\cap E)$

$=38-15=23$