Set Theory in Precalculus

Set theory is not normally covered in the curriculum because of time. However, set theory is a branch of Mathematics that deals with sets, subsets and collection of elements or objects. Below is a typical problem I would give my students when I first introduce set theory.

Problem: For the past weekend workshop conference, the conference had subject areas involving Math, Science and English. You will need to find out the number of students who participated at the weekend conference. Part of the information on the paper was damaged and the only information was given below. How many students altogether attended the weekend workshop.

* 5 students attended all three subject workshops

* 8 students attended only the Math and English workshops

* 7 students attended only the Math and Science workshops

* 9 students attended only the English and Science workshops

* !5 students registered for the Math workshop

* 14 students registered for the Science workshop

* 16 students registered for the English workshop

The difficult part of set theory is students don't normally see this type of problem in high school Mathematics. A lot of the times, Math for students is memorizing formulas and procedures to arrive at the correct answer. This type of problem ask you to formulate your thoughts and organize your thought process in such a way as to logically arrive at your answer. In this problem, it is not enough to say, I'll place the numbers in a formula and arrive at an answer. Thankfully, Venn diagrams allows you to organize information into sets where deduction can be used to arrive at the correct answer.

To help you with answering the question, below is a Venn Diagram for you to use.

Don Sabado


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