Answer to Question #265962 in Discrete Mathematics for Good heart

Question

Out of 300 students taking discrete mathematics 60 take coffee , 27 take coco, 36 take tea, 17 take tea only, 47 take chocolate only, 7 take chocolate and coco, 3 take chocolate tea and coco, 20 take coco only, 2 take tea, chocolate and coco, 30 take coffee only, 9 take tea and chocolate whereas 12 take 12 tea and coffe

Express this information on venn diagram

Find how many take beverages

Find how many take tea and coco

Answer 1

variables:

a = 12 - tea+coffee

b - tea+coco

c - coffee+tea+coco

d - coffee+coco

e = 7 - coco+chocolate

f = 3 - coco+tea+chocolate

g - tea+chocolate+coco+coffee

h - coco+chocolate+coffee

i = 9 - tea+chocolate

j = 2 - coffee+tea+chocolate

k - chocolate+coffee

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.