Venn diagram questions involve visual representations of the relationship between two or more different groups of things. Venn diagrams are first covered in elementary school and their complexity and uses progress through middle and high school.
This article will look at the types of Venn diagram questions that might be encountered at middle school and high school, with a focus on exam style example questions and preparing for standardized tests. We will also cover problem-solving questions. Each question is followed by a worked solution.
In middle school, sets and set notation are introduced when working with Venn diagrams. A set is a collection of objects. We identify a set using braces. For example, if set A contains the odd numbers between 1 and 10, then we can write this as:
Venn diagrams sort objects, called elements, into two or more sets.
This diagram shows the set of elements
sorted into the following sets.
Set A= factors of 10
Set B= even numbers
The numbers in the overlap (intersection) belong to both sets. Those that are not in set A or set B are shown outside of the circles.
Different sections of a Venn diagram are denoted in different ways.
ξ represents the whole set, called the universal set.
∅ represents the empty set, a set containing no elements.
Venn Diagrams Worksheet
Download this quiz to check your students' understanding of Venn diagrams. Includes 10 questions with answers!
Let’s check out some other set notation examples!
The intersection of \mathrm and \mathrm .
The union of \mathrm or \mathrm .
The complement of \mathrm
In middle school and high school, we often use Venn diagrams to establish probabilities.
We do this by reading information from the Venn diagram and applying the following formula.
For Venn diagrams we can say
In middle school, students learn to use set notation with Venn diagrams and start to find probabilities using Venn diagrams. The questions below are examples of questions that students may encounter in 6th, 7th and 8th grade.
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1. This Venn diagram shows information about the number of people who have brown hair and the number of people who wear glasses.
How many people have brown hair and glasses?
