A truth table is a logically-based mathematical table that illustrates the possible outcomes of a scenario. The truth table contains the truth values that would occur under the premises of a given scenario. As a result, the table helps visualize whether an argument is logical (true) in the scenario.
The rows of a basic truth table contain the Boolean logic true or false values, while the columns list the premises of a scenario as well as the conclusion. A simple truth table contains a single scenario and lists the valid statement and its negation.
How to Create a Truth Table
The first step in creating a truth table is to determine the number of variables and rows needed for the table and then write down all the possible combinations (typically diagrammed as "p" and "q").
For creating a basic "And" (conjunction) truth table, we'll use the following example:
"If you get accepted into State University, you'll get a six-figure job once you graduate."
In this example, "p" represents the first premise in which you get accepted into State University and "q" represents getting a six-figure job upon graduating.
The truth table will have a column for each of these premises and a third for the logical conclusion, with each row containing a logical result from the combination of the two premises, as shown in the illustration below:
The Five Basic Operations in Truth Tables
Truth tables use five basic operations:
1. Conjunction: An "and" operation where both arguments must be true in order for the statement itself to be true
2. Disjunction: An "or" operation where both arguments must be false in order for the statement itself to be false
3. Negation: A "not" operation is one that is the opposite (or complement) of the original value
4. Conditional: An "if - then" operation where the statement is false only when the first premise is true and the second is false
5. Bi-Conditional: An "if and only if" operation wherein the statement is true only when the premises share the same truth value (they're both either true or false)
Stay up to date on the latest developments in Internet terminology with a free weekly newsletter from Webopedia. Join to subscribe now.
The following facts and statistics capture the changing landscape of cloud computing and how service providers and customers are keeping up with... Read More »Facts about Computer Science: Education and Jobs
The following computer science facts and statistics provides a quick introduction to the changing trends in education and related careers. Read More »Text Messaging & Chat Abbreviations
From A3 to LOL and ZZZ this guide lists 1,500 text message and online chat abbreviations to help you translate and understand today's texting... Read More »
Learn about each of the five generations of computers and major technology developments that have led to the computing devices that we use... Read More »Computer Architecture Study Guide
Computer architecture provides an introduction to system design basics for most computer science students. Read More »Network Fundamentals Study Guide
Networking fundamentals teaches the building blocks of modern network design. Learn different types of networks, concepts, architecture and... Read More »