Question

venn diagram questions

Answer 1

Example 1: In a college, 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both tea and coffee.  

How many students like only tea?

How many students like only coffee?

How many students like neither tea nor coffee?

How many students like only one of tea or coffee?

How many students like at least one of the beverages?

Solution: The given information may be represented by the following Venn diagram, where T = tea and C = coffee.

Number of students who like only tea = 60

Number of students who like only coffee = 40

Number of students who like neither tea nor coffee = 20

Number of students who like only one of tea or coffee = 60 + 40 = 100

Number of students who like at least one of tea or coffee = n (only Tea) + n (only coffee) + n (both Tea & coffee) = 60 + 40 + 80 = 180

Answer 2

A Venn diagram is a diagram style introduced by John Venn that is used to represent the logical relationship between sets.

• Venn diagrams visually represent the similarities and differences between two concepts.
• Venn diagrams can be used to represent the relationship between sets, even if they are empty sets. This is one of the biggest advantages of the Venn diagram over Euler diagrams, which are almost the same except for this condition.
• Overlapping circles or other shapes are used in Venn diagrams to illustrate the relationships.
• Deciding the concepts to be compared is the first step of making a Venn diagram.
• Then the diagram is created by making a circle for each of the concepts in such a way that every circle should overlap with at least one other circle.
• Then, using the circles, the relation between the concepts is obtained.
• Circles that overlap share some characteristics in common, while circles that do not overlap do not share anything in common.

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