Solving the Venn Diagram Puzzle with Easy Steps

Many people encounter logic puzzles that might seem complex at first glance. However, with a strategic approach, these problems can be easily solved. One such puzzle involves 50 students who each drink either Coca-Cola or Pepsi, or both. In this article, we delve into how a Venn diagram can simplify this scenario and explain step-by-step how to solve it.

The Problem

Given a group of 50 students, 28 of them have drunk Coca-Cola, 32 have drunk Pepsi, and all students had at least one of these drinks. The question is: How many students drank both Coca-Cola and Pepsi?

This problem can be approached using set theory and the principles of Venn diagrams. A Venn diagram is a graphical representation used to describe relationships between sets. In this context, it will help us visualize the number of students who fall into each category.

Step-by-Step Solution

Understanding the Venn Diagram

A Venn diagram consists of overlapping circles that represent sets. In this puzzle, we will use two circles, one for Coca-Cola and one for Pepsi. The overlapping area represents the students who drank both beverages.

To start, let's denote the following:

C represents the set of students who drank Coca-Cola. P represents the set of students who drank Pepsi.

A Venn diagram will look like this:

Setting Up the Equations

The total number of students is 50. Let x represent the number of students who drank both Coca-Cola and Pepsi. This can be visualized in the overlapping area of the Venn diagram.

From the problem, we have the following information: C 28 (students who drank Coca-Cola) P 32 (students who drank Pepsi) Every student drank at least one drink.

We can set up the following equation based on the principle of inclusion-exclusion:

Total number of students Students who drank Coca-Cola Students who drank Pepsi - Students who drank both

50 28 32 - x

Calculating the Solution

Now, we can solve for x: [ 50 28 32 - x ]

Rearranging the equation to solve for x: [ x 28 32 - 50 ] [ x 60 - 50 ] [ x 10 ]

Hence, the number of students who drank both Coca-Cola and Pepsi is 10.

Conclusion

Using a Venn diagram and simple set theory, we were able to solve the logic puzzle efficiently. This method can be applied to various real-world problems involving overlapping sets and provides clearer insights into the relationships between different groups. By understanding the principles of Venn diagrams, you can tackle similar problems with confidence and ease.

Keywords

Venn Diagram, Logic Puzzles, Set Theory

This article explains how to solve a Venn diagram puzzle involving 28 students who had Coca-Cola and 32 who had Pepsi, with all students having at least one soft drink. The solution involves understanding Venn diagrams and using set theory principles.