Venn Diagram Math Example 4

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Example 4

medium
In a class of 30 students, 18 study French, 12 study Spanish, and 5 study both. How many study neither language?

Solution

  1. 1
    Use inclusion-exclusion for the union: ∣F∪S∣=18+12−5=25|F \cup S| = 18 + 12 - 5 = 25 students study at least one language.
  2. 2
    Students who study neither are outside both circles, so 30−25=530 - 25 = 5.

Answer

55 students study neither language.
A Venn diagram helps separate the overlap from the non-overlap. Subtracting the intersection once avoids double-counting students who study both languages.

About Venn Diagram

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

Learn more about Venn Diagram →

More Venn Diagram Examples

Example 1 easy

In a class of 30 students, 18 study French, 12 study Spanish, and 5 study both. Use a Venn diagram t

Example 2 medium

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

Example 3 medium

In a survey of 50 people, 30 like tea, 25 like coffee, and 10 like both. How many like only tea? Onl

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Related Concepts

SetUnionIntersection