Question 1119159: 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.
(a) How many students were taking mathematics, but neither English nor chemistry?
(b) How many were taking mathematics and chemistry, but not English?
(c) How many were taking English and chemistry, but not mathematics?
Answer by ikleyn(52787)   (Show Source):
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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.
(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.
Solved.
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In this solution, two-letter abbreviation means intersection of two sub-sets.
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