Venn Diagram Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
In a survey of 50 people, 30 like tea, 25 like coffee, and 10 like both. How many like only tea? Only coffee? Neither?

Solution

  1. 1
    Only tea: 30−10=2030 - 10 = 20. Only coffee: 25−10=1525 - 10 = 15.
  2. 2
    Total who like at least one: 20+10+15=4520 + 10 + 15 = 45.
  3. 3
    Neither: 50−45=550 - 45 = 5.

Answer

Only tea=20,  Only coffee=15,  Neither=5\text{Only tea} = 20,\; \text{Only coffee} = 15,\; \text{Neither} = 5
Subtract the overlap from each set to find the 'only' regions, then subtract the total union from the universal set.

About Venn Diagram

A diagram using overlapping circles to visually represent sets and their relationships such as union, intersection, and complement.

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More Venn Diagram Examples

Example 1 easy

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Example 2 medium

Given [formula], [formula], [formula], find [formula] using the inclusion-exclusion principle.

Example 4 medium

In a class of 30 students, 18 study French, 12 study Spanish, and 5 study both. How many study neith

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Related Concepts

SetUnionIntersection