Problem 3

Problem 3

Solve a problem using a Venn diagram involving 3 attributes

It is time for our third problem:

Here is some information about a class of 16 students:

  • 13 students study Italian.

  • 12 students study German.

  • 10 students study French.

  • 8 students study Italian and French.

  • 9 students study Italian and German.

  • 9 students study German and French.

  • Every student studies at least one of these languages.

How many students study Italian, German and French?

The Venn diagram for this problem will include 3 circles. Have a go at drawing it then expand the sections below.

Notice that 2 numbers have been included in the diagram. There are 16 students in the class and every student studies at least one of the 3 languages.

Venn diagram with 3 overlapping circles (Italian, French, German); 16 is ourside the diagram and 0 outside the circles.

The diagram below is annotated with some information.

Venn diagram with 3 overlapping circles (Italian, French, German); 16 is ourside the diagram and 0 outside the circles. The parts of the circles are labelled.

  1. Can you see which parts of the problem provide us with the information annotated on the diagram?

  2. There are 9 students who study Italian and German. Which 2 parts of the Venn diagram must add to 9?

  3. There are 13 students studying Italian. Which 4 parts of the Venn diagram must add to 13?

Work with a partner and use trial and error. Find the correct answer that makes the numbers in a 3 attribute Venn diagram add to 16?

  • 13 students study Italian.

  • 12 students study German.

  • 10 students study French.

  • 8 students study Italian and French.

  • 9 students study Italian and German.

  • 9 students study German and French.