SOLUTION: In a srvey,80 computerscience teachers were asked which of the three programming languages, Pascal,Fortran and C,have they used to introduce programming to students.40 teachers sai

Question 38180: In a srvey,80 computerscience teachers were asked which of the three programming languages, Pascal,Fortran and C,have they used to introduce programming to students.40 teachers said they have used Pascal,35 said they have used Fortran,25 said they have used C,20 said they have used both Pascal and Fortran,17 said they have used Pascal and C, 5 said they have used Fortran and C,and 3 said they have used all the three languages.
a)How many teachers have used Fortran alone?
b)How many teachers have used both Pascal and C?
c)How many teachers have used Fortran, but not C?
d)How many used none of the three languages?

Answer by khwang(438) (Show Source):
You can put this solution on YOUR website!

Given P = 40, F = 35, C = 25.
P^F = 20, P^C = 17, F^C= 5, P^F^C = 3.

A diagram wiil be helpful.
a) Use F alone: F - (F ^ P) - (F ^ C ) + P^F^C= 35 - 25 + 3 = 13.
b) 17 use both P and C , P^C - P^F^C = 17 - 3 = 14 use P & C only
c) F - F^C = 35 - 5 = 30
d) The formula about inclusion-exclusion: (or Venn diagram)
P U F U C = P + F + C - (P^F + P^C+ F^C) + P^F^C
= 40 + 60 - 42 + 3 = 61.
the complement (P U F U C )' = 80 - 61 = 19... using none of three
khwang