Solution to d)Out of 300 students taking discrete mathematics ,60 take coffee, 27take cocoa,36 take tea,17 take … - Sikademy
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Archangel Macsika

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

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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.

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Question ID: mtid-5-stid-8-sqid-3405-qpid-2104