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Jan Meyer
2026-04-07 13:34:22 +02:00
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10 Courses/01 - WiSe 2025_26/DAS/Logic.md Normal file
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## 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 | $not xor$ |