Answer to Question #163773 in Discrete Mathematics for Toye

Question

If 11 students offer Biology, 13 students offer Maths, 14 students offer Agric, 9 students offer Maths and Biology, 3 students offer Maths and Agric, 7 students offer Maths, Biology and Agric. How many students offer Biology and Agric?

Answer 1

Let the total number of students be $S$ and the numbers of student offering Biology and Maths be $x$ .

$S=n(B)+n(M)+n(A)+n(B\bigcap M)+n(B \bigcap A)+n(M\bigcap A)+n(B\bigcap M\bigcap A)\\ S=11+13+14+x+9+3+7\\ S=57+x\\ x=S-57$