EMAT 6700

by Brad Simmons

Venn Diagrams

Use geometer's sketchpad to create Venn diagrams.

Venn Diagrams use circles to represent sets of objects.  Furthermore, they show how different sets of data are related.  Venn diagrams are very useful in explaining conditional statements.

Consider the set of real numbers and some subsets of the set of real numbers.  

By using the Venn diagram it is easier to explain that if a number is in the set of whole numbers, then it is also in the set of integers, rational numbers, and real numbers.  Likewise, it is easier to explain that a whole number may or may not be a natural number and a natural number is definitely not an irrational number.  

Venn diagrams make it easy to compare sets of data.  What do whole numbers and irrational numbers have in common?  They are both in the set of real numbers.

Problem #1: Use geometer's sketchpad to create a Venn diagram to show how the centerfielder on a baseball team belongs to at least four sets or subsets of people.

For a sketch that shows a possible answer to problem #1 please click here.

Problem #2: Use geometer's sketchpad to create a Venn diagrams that represents the conditional statement, "if a person is a school teacher, then the person wants young people to be successful."

For each statement, create a Venn diagram using geometer's sketchpad.  Then write the sentence in if-then form.

Problem #3: Every dog has long hair.

Problem #4: People who live in Nebraska like corn.

Problem #5: All integers are rational numbers.

Problem #6: Stephens County Indians wear red and black.