Answer to Question #160598 in Discrete Mathematics for Sudarshan

Question

In a school, students must take at least one of these subjects: Maths, Physics or Chemistry. In a group of 50 students, 7 take all three subjects, 9 take Physics and Chemistry only, 8 take Maths and Physics only and 5 take Maths and Chemistry only. Of these 50 students, x take Maths only, x take Physics only and x + 3 take Chemistry only. Draw a Venn diagram, find X i and hence find the number taking Maths.

Answer 1

Venn diagram:

There are 50 students in a group.

Using Venn diagram, we have $50=x+8+7+5+x+9+(x+3)$ .

$50=3x+32$

$3x=18$

$x=6$

The number of students that take Maths is $x+8+7+5=26$ .

Answer: $x=6$ ; $26$ students take Maths.