## Operators 
| Operation         | Explanation                          | Notation  |
| ----------------- | ------------------------------------ | --------- |
| **and**<br>       | Both $p$ and $q$ must be true        | $p and q$ |
| **or**            | Either $p$ or $q$ (or both) are true | $p or q$  |
| **not**           | Negates the statement                | $not p$   |
| **Implication**   | If $p$ then $q$                      | $=>$      |
| **Biconditional** | $p$ if and _only_ if $q$             | $<=>$     |
| **xor**           | Either $p$ or $q$ but not both       | $xor$     |
### Implied Operators
| Operation | Explanion                               | Notation       |
| --------- | --------------------------------------- | -------------- |
| **nand**  | $p$ and $q$ are not both true           | $not(p and q)$ |
| **nor**   | neither of $p$ and $q$ are true         | $not(p or q)$  |
| **xnor**  | $p$ and $q$ are both false or both true | $not xor$      |