# Definition:Truth Table/Number

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## Definition

The **truth table number** of the truth table of a statement form is a string consisting of the truth values in numerical form of the main connective.

The order in which the **truth table number** is presented is usually in ascending or descending numerical order of the truth values of the simple statements contributing to that statement form, either:

- Ascending order: $00, 01, 10, 11$, that is: $\F\F, \F\T, \T\F, \T\T$

or:

- Descending order: $11, 10, 01, 00$, that is: $\T\T, \T\F, \F\T, \F\F$

Which format is being used needs to be specified.

Hence the **truth table number** can be found by reading either **up** or **down** the column holding the main connective in the truth table of the statement form.

## Also known as

The **truth table number** can be seen hyphenated: **truth-table number**.

Some sources refer to it as the **matrix number**.

## Sources

- 1959: A.H. Basson and D.J. O'Connor:
*Introduction to Symbolic Logic*(3rd ed.) ... (previous) ... (next): $\S 2.5$: Further Logical Constants