Truth Tables
A convenient way of analyzing the truthfulness of a statement is by describing it using a truth table. A truth table lists all the possible cases for all the involved variables $p, q, r, \dots$ in the statement and finds whether the statement as a whole is true or false in each such case.
To get started with truth tables, let's first describe the $6$ logical operators that we listed on slide 4, one truth table per operator example. This currect slide shows the first 3 of the operators. In our truth tables, $1$ means 'true' and $0$ means 'false':
| $p$ |
$\boldsymbol{\neg p}$ |
| $0$ |
$1$ |
| $1$ |
$0$ |
Truth table for negation: $\neg p$
| $p$ |
$q$ |
$\boldsymbol{p \wedge q}$ |
| $0$ |
$0$ |
$0$ |
| $0$ |
$1$ |
$0$ |
| $1$ |
$0$ |
$0$ |
| $1$ |
$1$ |
$1$ |
Truth table for conjunction: $p \wedge q$
| $p$ |
$q$ |
$\boldsymbol{p \vee q}$ |
| $0$ |
$0$ |
$0$ |
| $0$ |
$1$ |
$1$ |
| $1$ |
$0$ |
$1$ |
| $1$ |
$1$ |
$1$ |
Truth table for disjunction: $p \vee q$
These notes by Miriam Briskman are licensed under CC BY-NC 4.0 and based on sources.