Answer to Question #348312 in Discrete Mathematics for Lance

Question

A survey of 100 college students revealed the following information about their enrolment in Mathematics, Political Science, and Sociology courses. Twenty-six take Mathematics; 65 take Political Science; 65 take Sociology; 14 take Mathematics and Political Science; 13 take Mathematics and Sociology; 40 take Political Science and Sociology; 8 take Mathematics, Political Science and Sociology. How many students are taking both Mathematics and Sociology but not Political Science?

Answer 1

We can use an Euler diagram to answer this question.

We know that 8 students take Mathematics, Political Science and Sociology - it's the intersection area of three circles.

Also we know that 13 students take Mathematics and Sociology - it's the shaded intersection area of two circles (Mathematics and Sociology).

To find number of students taking both Mathematics and Sociology but not Political Science, we can subtract 8 from 13:

$13-8=5.$

Answer: 5 students take both Mathematics and Sociology but not Political Science.