Question

Out of 100 students, we consider the sets `S of those who

study sociology, ´E of those who study economics and ´G of those who study

study management. Of these 100 students, 55 study sociology, 9 social

sociology and management, 7 sociology and economics, 8 economics and management, 6

sociology and management but not economics, 80 sociology or management and

12 economy only.

(i) How many students take the three subjects?

(ii) How many are studying management?

(iii) How many are studying economics?

(iv) How many do not study any of these 3 subjects?

Answer 1

Hi,

Explanation:

`#(S\ \cap\ G)=9\\#( (S\ \cap\ G) -\ E)=6\\\Longrightarrow\ #(S\ \cap\ G\ \cap\ E) =9-6=3\ if\ social\ sociology\ is\ the \ same\ as\ sociology\\\\#(E\ \cap\ G)=8 \Longrightarrow\ #( (E\ \cap\ G) -\ S)=8-3=5\\\\#(S\ \cap\ E)=7 \Longrightarrow\ #( (S\ \cap\ E) -\ G)=7-3=4\\...`