Venn Diagrams: Three-Set Problems

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Questions and Answers

In a survey of 100 people, 60 like apples, 50 like bananas, and 20 like neither. How many people like both apples and bananas?

30 people like both apples and bananas.

A group of 50 students were surveyed about their favorite subject. 25 liked math, 20 liked science, and 8 liked both. How many students liked neither math nor science?

13 students liked neither math nor science.

In a class of 40 students, 22 are in the Math Club and 18 are in the Science Club. If 6 students are in both clubs, how many students are in neither the Math Club nor the Science Club?

6 students are in neither club.

Of 80 dogs at a vet clinic, 35 have fleas, 25 have ticks, and 10 have both fleas and ticks. How many dogs have either fleas or ticks, but not both?

<p>50 dogs have either fleas or ticks, but not both.</p> Signup and view all the answers

In a group of 75 people, 32 like coffee, 40 like tea, and 12 like neither. How many people like both coffee and tea?

<p>9 people like both coffee and tea.</p> Signup and view all the answers

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Flashcards

Venn Diagrams

Visual tools showing relationships between sets, useful for solving set-related problems.

Region 1 (Venn Diagram)

Represents elements in set A but not in set B within a Venn diagram.

Intersection (A ∩ B)

The overlapping area in a Venn diagram where elements belong to both set A and set B.

Region 3 (Venn Diagram)

Represents elements belonging to set B but not to set A within a Venn diagram.

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Region 4 (Venn Diagram)

Elements in the universal set but not in set A or set B.

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