Truth Tables
Here are the truth tables for the remaining 3 operator examples:
| $p$ |
$q$ |
$\boldsymbol{p \oplus q}$ |
| $0$ |
$0$ |
$0$ |
| $0$ |
$1$ |
$1$ |
| $1$ |
$0$ |
$1$ |
| $1$ |
$1$ |
$0$ |
Truth table for exclusive disjunction: $p \oplus q$
| $p$ |
$q$ |
$\neg p$ |
$\boldsymbol{p \to q\;(= \neg p \vee q)}$ |
| $0$ |
$0$ |
$1$ |
$1$ |
| $0$ |
$1$ |
$1$ |
$1$ |
| $1$ |
$0$ |
$0$ |
$0$ |
| $1$ |
$1$ |
$0$ |
$1$ |
Truth table for implication: $p \to q$
| $p$ |
$q$ |
$\neg p$ |
$\neg q$ |
$p \to q \;(= \neg p \vee q)$ |
$q \to p \;(= \neg q \vee p)$ |
$\boldsymbol{p \leftrightarrow q \;(= (p \to q) \wedge (q \to p))}$ |
| $0$ |
$0$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
| $0$ |
$1$ |
$1$ |
$0$ |
$1$ |
$0$ |
$0$ |
| $1$ |
$0$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
| $1$ |
$1$ |
$0$ |
$0$ |
$1$ |
$1$ |
$1$ |
Truth table for the biconditional: $p \leftrightarrow q$
These notes by Miriam Briskman are licensed under CC BY-NC 4.0 and based on sources.