# truth table

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:

p | q | Result |
---|---|---|

T |
T |
T |

T |
F |
F |

F |
T |
F |

F |
F |
F |

**The Five Basic Operations in Truth Tables**

Truth tables use five basic operations:

** 1. Conjunction:** An "and" operation where both arguments must be

**in order for the statement itself to be**

*true*

*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)

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