# Discrete Math

A professor gave his 40 students a test with three questions. Every student answered at least one question. Ten didn't answer the first question. 14 didn't answer the second question. 12 didn't answer the third question. If 18 students answered all three questions, how many answered exactly one question?

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(3 * 40) - (3 * 18) - 10 - 14 - 12 = 2 t + x

40 - 18 = t + x

solve the system for x

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2. Another way to solve.
Let
A=# of students who answered the first question
B=# of students who answered the second question
C=# of students who answered the third question

Then
we are given
B+C-|B∩C| = 10
A+C-|A∩C| = 14
A+B-|A∩B| = 12
2A+2B+2C-(|A∩B|+|B∩C|+|C∩A|)=36....(1)

But the total number who answered one OR two question is 40-18=22, or
A+B+C-|A∩B|- |B∩C|-|C∩A|=22.....(2)

(1)-(2)
A+B+C=36-22=14

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