Answer to Question #115138 in Discrete Mathematics for Germain Adadey

Question

A number of science students prepared for examination in physics, chemistry and mathematics. Out of the number 15 took physics,23 took Maths and 20 took chemistry. 6 took physics and maths, 9 took maths and chemistry. all those who took physics also took chemistry. One of the students felt ill and fail to write the exams. How many students toa number of science students prepared for examination in physics, chemistry and mathematics. Out of the number 15 took physics,23 took Maths and 20 took chemistry. 6 took physics and maths, 9 took maths and chemistry. all those who took physics also took chemistry. One of the students felt ill and fail to write the exams. A. How many students took exactly one of the subjects? B. how many students took exactly two of the subjects? C. How many students prepare for the examination?

Answer 1

N(P)-took physics,N(C)-took chemistry,N(M)-took maths

all those who took physics also took chemistry, so

N(P&C)=N(P)-N(P&M)=15-6=9

a)exactly one subject

N=N(P)-(N(P&M)+N(P&C))+N(C)-(N(C&M)+N(P&C))+N(M)-(N(P&M)+N(M&C))+=0+23-(6+9)+20-(9+9)=10

b)exactly two subjects

N=N(P&M)+N(C&M)+N(P&C)=6+9+9=24

c) N=N(P)+N(C)+N(M)-N(P&C)-N(P&M)-N(M&C)+1=20+23+15-6-9-9+1=35