Venn Diagram Logic Problem Tutorial 2v2c6x

Venn Diagrams Solving Logic Problems Using Venn Diagrams

Venn Diagram Logic Problems Explained Venn diagram logic problems basically gives two or three classifications with the addition of many numbers. With the given information provided, you populate the diagram to determine the remaining information.

A Venn Diagram Logic Problem Here is an example of a Venn Diagram logic problem: Out of forty students, there are 14 who are taking Physics and 29 who are taking Calculus. How many students are not in either class if five of the students are in both classes? How many students are in either class? And, what is the probability that a randomly chosen student from

Solving the Venn Diagram Logic Problem So, we have two classifications in this universe (the enclosing rectangle represents the “universe”) which are: Physic students and Calculus students. First, we draw our universe for the forty students with two overlapping Physics: 14 circles: Calculus: 29

Solving the Venn Diagram Logic Problem (cont.) There are 5 students who are taking both classes, so the 5 will go in the overlap: Physics: 14

Calculus: 29

5

Solving the Venn Diagram Logic Problem (cont.) Now, the 5 students of the 14 Physics students has been ed for. So, that leaves nine students taking Physics but NOT Calculus so the “9” will go 14 Calculus: 29 in the PhysicsPhysics: circle. 9

5

Solving the Venn Diagram Logic Problem (cont.) Five of the 29 Calculus students have been ed for which leaves 24 students taking Calculus but NOT Physics. So, the 24 goes in the Calculus Physics: 14 Calculus: 29 circle. 9

5

24

Solving the Venn Diagram Logic Problem (cont.) This tells us that a total of 9 + 5 + 24= 38 students who are in either Physics or Calculus (or both). So, this leaves two students who are uned for which means these two are taking neither class. Physics: 14

9

2 5

Calculus: 29 24

Venn Diagram Logic Problem Solved From our populated Venn Diagram, we have the answers to the questions (from slide 3).

There are two students who are taking neither class. In at least one of the classes, there are 38 students. The probability student Physics:of 14a randomly Calculus:chosen 29 2 taking Calculus but NOT in this group who is Physics is 24/40 =50.6 =2460%. 9