## Construct a venn diagram, Mathematics

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In a survey of 85 people this is found that 31 want to drink milk 43 like coffee and 39 wish tea.  As well 13 want both milk and tea, 15 like milk & coffee, 20 like tea and coffee and 12 like none of the three drinks.  Find out the number of people who want all the three drinks.  Display the answer by using Venn Diagram.

Ans:  Let A, B and C is set of people who wish to drink milk, take coffee and take tea correspondingly. So |A| = 31, |B| = 43, |C| = 39, |A∩B| = 15, |A∩C| = 13, |B∩C| = 20, |A∪B∪C| = 85 - 12 = 73. Hence, |A∩B∩C| = 73 + (15 + 13 + 20) - (31 + 43 + 39) = 8. 24x+7=3x+10

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