Answer to Question #140410 in Discrete Mathematics for James macharia

Question #140410
Out of 300 students taking discrete mathematics, 60 take coffee, 27 take 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, 9 take tea and chocolate whereas 12 take tea and coffee . Express this information on a venn diagram.
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Expert's answer
2020-10-27T20:08:33-0400

We note from the diagram below no. of tea drinkers =17+a+b+c+d+e+f=36.=17+a+b+c+d+e+f=36. Hence a+b+c+d+e+f=3617=19.a+b+c+d+e+f= 36-17=19. Also cocoa and chocolate =d+e+h+i=7.=d+e+h+i=7.

Hence a+b+c+d+h19+7=26.a+b+c+d+h\leq 19+7=26. Also cocoa drinkers 20+b+d+g+h+i+e=27b+d+g+h+i+e=7.20+b+d+g+h+i+e=27\Rightarrow b+d+g+h+i+e=7. Hence

b+g+(d+e+h+i)=7b+g+7=7b=g=0.b+g+(d+e+h+i)=7\Rightarrow b+g+7=7\Rightarrow b=g=0. Hence a+b+c+d+h+g26+0=26.a+b+c+d+h+g\leq 26+0=26. But no of coffee drinkers =60. Whereas no. of coffee drinkers is 30+a+b+c+d+g+h26+30=56.30+a+b+c+d+g+h\leq 26+30=56\Rightarrow \Leftarrow .

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Comments

Assignment Expert
24.02.21, 16:23

Dear Sahil Gupta, please use the panel for submitting a new question. It is necessary to provide the full description of the question so that our experts could help you.

Sahil Gupta
17.02.21, 13:03

This is the exact same question but waana add 2 more questions in it which is 2.)Find how many take beverages 3.) Find how many take cocoa & tea

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