Introduction to Truth Tables

Truth tables are a fundamental tool in logic and mathematics, used to determine the validity of logical statements and to analyze complex logical expressions. By systematically evaluating the truth values of propositions, truth tables help us understand how different logical operators interact. This article presents three practical examples of using truth tables to solve logical problems, demonstrating their application in diverse scenarios.

Example 1: Evaluating a Simple Logical Expression

Context

In this example, we will evaluate the logical expression P AND Q to determine its truth values under various conditions. This scenario could arise in a situation where two conditions must both be true for an action to take place, such as whether a student passes a course based on attendance (P) and exam scores (Q).

P	Q	P AND Q
True	True	True
True	False	False
False	True	False
False	False	False

In this truth table:

When both P and Q are true, P AND Q is true.
In all other cases, P AND Q is false.

Notes

This example highlights the necessity of both conditions being satisfied for the overall expression to hold true. Variations could include using OR (P OR Q) or NOT (NOT P) to explore other logical scenarios.

Example 2: Analyzing Conditional Statements

Context

This example examines the logical statement