Question

d)Out of 300 students taking discrete mathematics ,60 take coffee, 27take cocoa,36 take tea,17 take tea only,47 take chocolate only,7 take chocolate and cocoa,3 take chocolate, tea and cocoa,20 take cocoa only ,2 take tea, coffee and Chocolate, 30 take coffee only ,9take tea and chocolate whereas 12 take tea and coffee. 

i)Express this information on a Venn diagram                                                                

 ii) Find how many Take beverages                                                                                                    

 iii) Find how many take cocoa and tea                                                                   

Answer 1

From the diagram above, the number of tea drinkers is

$17+a+b+c+f+g+i+j=36\\ a+b+c+f+g+i+j=19.............(1)$

Also, cocoa and chocolate is

$e+f+g+h=7.......(2)$

Cocoa drinkers are

$20+b+c+d+e+f+g+h=27\\ b+c+d=0\\ \implies b=c=d=0$

We can implies from (1) and (2) that $a+f+g+h+j+k\leq26$

Numbers of coffee drinkers are

$30+a+c+d+g+h+j+k=30+a+g+h+j+k\leq 30+26=56 \neq 60$

This is a contradiction

Number of Tea and Coffee drinkers cannot be defined.