Answer to Question #266738 in Discrete Mathematics for Bjoy

Question

Refer to a group of 191 students, of which 10 are taking math, business, and language; 36 are taking math and business; 20 are taking math and language; 18 are taking business and language; 65 are taking math; 76 are taking business and 63 are taking language.

26-30. Illustrate the Venn Diagram

Answer 1

$$N(M\cup B\cup L)=N(M)+N(B)+N(L)$$

$$-N(M\cap B)-N(M\cap L)-N(B\cap L)$$

$$+N(M\cap B\cap L)=65+76+63$$

$$-36-20-18+10=140$$

$$191-140=51$$