Sets and Venn Diagrams

Even as an adult, understanding sets; the unions, intersections, complements, empty sets, and universal sets is extremely complicated to understand. Through the course I am taking this semester, I have learned how to use a Venn Diagram to help students better understand sets and the questions that come with them.

The first thing students need to understand is what an Universal Set is; in easiest terms is a set that contains all elements of a problem to be considered.

I took away the Venn Diagram to show that a Universal Set is just all of the numbers all together.

A Union of two sets, denoted by a capital U, is everything in both sets. Now I now as an elementary student, this is difficult to understand (mentally and visually). But, if you explain the same definition with a Venn Diagram, your students will better understand.

For this example, set A={2,5,7} and set B={1,2,5,8}

When asked what the Union of A and B is you would state every single number from both sets like such: AUB= {1,2,5,7,8}

An Intersection of two sets, denoted by a capital upside down U, is anything that appears in both sets; the elements in the middle of both sets. Again, for students reading this or hearing a teacher explains this, would be very complicated to understand, so if you demonstrate a Venn Diagram they can better understand.

For this example, set A={1,2,3,4,5} and set B={1,3,9,12}

When asked what the Intersection of A and B is you would state that the numbers in the middle of the two sets like such: A∩B= {1,3}

A Complement of a set is all the elements in the universal set that are not  in the initial set, and is denoted with a letter c.

In this example, the Complement of  set M would be any numbers outside of the set in yellow, and would be stated as such: Mc={-5,-4,-3,-2,-1,0,1,3,5,6}

Lastly, an Empty Set is a set that has no elements, is often referred to as a Null Set or Disjoint Set, and is notated with {} or a zero with a line through it.