Answer to Question #145233 in Discrete Mathematics for Godfred Kingdom

Question

in a class of 35 students, each student studies Chemistry or woodwork. Twice as many study chemistry as study woodwork and half as many study only chemistry as study both. illustrate the information on a venn diagram and hence find the number of students who study both subjects.

Answer 1

let set A be the set of students studying chemistry, and let set B be the group of students studying woodwork.

n(A) = 2x , n(B) = x

n(A$\cap$B) =$\dfrac{2n(A)}{3}$ = 4/3x

n(A$\cap$B) > n(B) which is impossible because the number of students studying both subjects cannot be greater than the number of students studying one subject.