Venn Diagram Math Example 1

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easy

In a class of 30 students, 18 study French, 12 study Spanish, and 5 study both. Use a Venn diagram to find how many study neither language.

1
Let $F$ = French students, $S$ = Spanish students. Place $|F \cap S| = 5$ in the overlap region.
2
French only: $18 - 5 = 13$ . Spanish only: $12 - 5 = 7$ . So $|F \cup S| = 13 + 5 + 7 = 25$ .
3
Students studying neither: $30 - 25 = 5$ .

Answer

5 \text{ students study neither language}

A Venn diagram partitions the universal set into non-overlapping regions. The inclusion-exclusion principle gives

|F \cup S| = |F| + |S| - |F \cap S|

About Venn Diagram

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

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

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

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