Truth Tables

Also known as: truth table

principle

A table listing all possible combinations of boolean inputs and their corresponding outputs for a logical expression. Foundation of digital logic, circuit design, and formal reasoning about program correctness.

💡 Intuition

Map out every possible True/False scenario to be sure you understand what a logical expression does.

Core Idea

Truth tables exhaustively verify logical expressions and can reveal equivalences between different expressions.

🔬 Example

AND table: T,T→T; T,F→F; F,T→F; F,F→F. Exactly one row gives True.

🎯 Why It Matters

Foundation of digital logic, circuit design, and formal reasoning about program correctness.

⚠️ Common Confusion

With n variables there are 2ⁿ rows — 3 variables means 8 rows, 4 means 16.

Related Concepts

Prerequisites

boolean logic logical operators

How Truth Tables Connects to Other Ideas

To understand truth tables, you should first be comfortable with boolean logic and logical operators.

Go Deeper

Formula Explained

Notation, derivation, and common mistakes

Frequently Asked Questions

What is Truth Tables in CS Thinking?

A table listing all possible combinations of boolean inputs and their corresponding outputs for a logical expression.

Why is Truth Tables important?

Foundation of digital logic, circuit design, and formal reasoning about program correctness.

What do students usually get wrong about Truth Tables?

With n variables there are 2ⁿ rows — 3 variables means 8 rows, 4 means 16.

What should I learn before Truth Tables?

Before studying Truth Tables, you should understand: boolean logic, logical operators.