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.
From keyword analysis to backlinks and Google search engine algorithm updates, our search engine optimization glossary lists 85 SEO terms you need... Read More »Slideshow: History of Microsoft Operating Systems
Microsoft Windows is a family of operating systems for personal computers. In this article we look at the history of Microsoft operating... Read More »Slideshow: Interesting Facts About Google Search
From Goats to Penguins, a server outage and trillions of searches, our slideshow presents interesting facts about Google and the Google.com... Read More »
Java is a high-level programming language. This guide describes the basics of Java, providing an overview of syntax, variables, data types and... Read More »Java Basics, Part 2
This second Study Guide describes the basics of Java, providing an overview of operators, modifiers and control Structures. Read More »The 7 Layers of the OSI Model
The Open System Interconnection (OSI) model defines a networking framework to implement protocols in seven layers. Use this handy guide to compare... Read More »