# Logische Operatoren ##### **Wahrheitstabelle**
**A** **B** **A AND B** **A NAND B** **A OR B** **A NOR B** **A XOR B** **A XNOR B** **NOT A**
0 0 0 1 0 1 0 1 1
1 0 0 1 1 0 1 0 0
0 1 0 1 1 0 1 0 1
1 1 1 0 1 0 0 1 0
##### **Mathematische und Technische Symbolik**
**Operator** **Formel ****Schaltsymbolik ****Relaislogik **
**AND** ![Y=A\wedge B](https://wikimedia.org/api/rest_v1/media/math/render/svg/4aaa76443c197f6f63f9a6ae46a7b06a01509079) [![IEC_AND_label.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/BCOounzBojICJaoL-iec-and-label-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/BCOounzBojICJaoL-iec-and-label-svg.png)[![Relay_and.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/C8FWypP7AoOVcOZd-relay-and-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/C8FWypP7AoOVcOZd-relay-and-svg.png)
**NAND** ![{\displaystyle Y=A\;\;\!\!{\overline {\wedge }}\;\;\!\!B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69c47195b8205e66ec9b96afa25162174e8febcb)[![IEC_NAND_label.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/90rSaZeZO3HERQII-iec-nand-label-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/90rSaZeZO3HERQII-iec-nand-label-svg.png)[![Relay_nand.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/3LhaHdBEy9Yg671w-relay-nand-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/3LhaHdBEy9Yg671w-relay-nand-svg.png)
**OR** ![{\displaystyle Y=A\lor B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/541c39c440818b758708ad80ecb5f39ea3a7b769)[![IEC_OR_label.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/rx267MtYXIx1kVFs-iec-or-label-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/rx267MtYXIx1kVFs-iec-or-label-svg.png)[![Relay_or.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/4OIBX24ozpsd3ce7-relay-or-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/4OIBX24ozpsd3ce7-relay-or-svg.png)
**NOR** ![{\displaystyle Y=A\;\;\!\!{\overline {\vee }}\;\;\!\!B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ad15f155b85d26d51e3bba096c4c24e7a2e89cb)[![IEC_NOR_label.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/bCpfcsTQ3iPnylXH-iec-nor-label-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/bCpfcsTQ3iPnylXH-iec-nor-label-svg.png)[![Relay_nor.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/gxAScOOOLs2FhVWr-relay-nor-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/gxAScOOOLs2FhVWr-relay-nor-svg.png)
**XOR** ![Y = A \,\underline{\lor}\, B](https://wikimedia.org/api/rest_v1/media/math/render/svg/42715f34fe31f2f82e16a7de6289667391a0f4c0)[![IEC_XOR_label.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/gSbz9lqwcGb6r15k-iec-xor-label-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/gSbz9lqwcGb6r15k-iec-xor-label-svg.png)[![Relay_xor.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/7WGkUllzbhOFg92S-relay-xor-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/7WGkUllzbhOFg92S-relay-xor-svg.png)
**XNOR** ![Y = A \,\overline{\underline{\lor}}\, B](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1f372a2d00f45434f3282c1e4573d7c937367c0)[![IEC_XNOR_label.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/7hLvvrcqB8nKgT8K-iec-xnor-label-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/7hLvvrcqB8nKgT8K-iec-xnor-label-svg.png)[![Relay_xnor.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/UCUdqELzaiU4UuvU-relay-xnor-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/UCUdqELzaiU4UuvU-relay-xnor-svg.png)
**NOT** ![Y = \overline{A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c605d03f8856bc64dd8c918c0186e454b4c84486) [![IEC_NOT_label.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/Z7gm6nYpdFTBf96U-iec-not-label-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/Z7gm6nYpdFTBf96U-iec-not-label-svg.png)[![Relay_not.svg.png](https://doku.stnd.io/uploads/images/gallery/2022-08/scaled-1680-/iUYZvC3tYpcim2lS-relay-not-svg.png)](https://doku.stnd.io/uploads/images/gallery/2022-08/iUYZvC3tYpcim2lS-relay-not-svg.png)