Question

dOut 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 Express this information on a Venn diagram​

Answer 1

Here the sets are overlapping. Overlapping sets are those which contain at least one element common.

The  four sets of  coffee, tea, chocolate and cocoa users all are overlapping containing one or more elements of the other.

The missing set numbers have been marked as a, b, c, d in the diagram.

The data in the question tells that

60 take coffee,

30 take coffee only

2 take tea, coffee and Chocolate,

whereas 12 take tea and coffee

17 take tea only,

2 take tea, coffee and Chocolate,

3 take chocolate, tea and cocoa,

whereas 12 take tea and coffee

36 take tea,

9 take tea and chocolate

47 take chocolate only

7 take chocolate and cocoa

3 take chocolate, tea and cocoa,

2 take tea, coffee and Chocolate,

9 take tea and chocolate

20 take cocoa only

27 take cocoa

3 take chocolate, tea and cocoa,

7 take chocolate and cocoa

Total tea takers= T= { 17+12+9+2+3+a+b}= {43+a+b}

Total coffee takers= C= {30+12+2+a+b+c+d}= {44+a+b+c+d}

Total Chocolate users= Ch= {47+9+3+2+7+b+c} = {68+b+c}

Total Cocoa users= Co= { 20+7+3+a+b+c+d}= {30+a+b+c+d}

C∩ Co= {d}

C∩ T= {12}

T ∩ Ch= {9}

Ch∩ Co= {7}

This can be shown by the Venn diagram as follows.

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