Answer to Question #282812 in Discrete Mathematics for Kapil kurmi

Question

One hundred students were asked whether they had taken course in any of the three areas, CSE,

ME and EE. The results were.

45 had taken CSE, 38 had taken ME, 21 had taken EE, 18 had taken CSE and ME, 9 had

taken CSE and EE, 4 had taken ME and EE and 23 had taken no courses in any of the three

areas.

(i) Draw a Venn diagram that will show the results of the survey?

(ii) Determine the number K of students who had taken courses in exactly?

b) One of the areas b) Two of the areas c) Nor in CSE, nor in ME but in EE

Answer 1

(i)

$$N(CS\cup M\cup E)+N(\overline{CS\cup M\cup E})=N(U)$$

$$N(CS\cup M\cup E)=100-23=77$$

$$N(CS\cup M\cup E)=N(CS)+N(M)+N(E)$$

$$-N(CS\cup M)-N(CS\cup E)-N(M\cup E)$$

$$+N(CS\cap M\cap E)$$

$$N(CS\cap M\cap E)=77-45-38-21$$

$$+18+9+4=4$$

(ii)

a)

$$N(only\ one)=N(only\ CS)+N(only\ M)$$

$$+N(only\ E)=22+20+12=54$$

b)

$$N(only\ two)=5+14+0=19$$

c)

$$N(only\ E)=12$$