| 0,0 | 0,1 | 1,0 | 1,1 | (p,q) | |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | ⤫ | false |
| 0 | 0 | 0 | 1 | ⤭ | AND |
| 0 | 0 | 1 | 0 | ⤫ | https://en.wikipedia.org/wiki/Material_nonimplication |
| 0 | 0 | 1 | 1 | ⤫ | p |
| 0 | 1 | 0 | 0 | ⤫ | https://en.wikipedia.org/wiki/Converse_nonimplication |
| 0 | 1 | 0 | 1 | ⤫ | q |
| 0 | 1 | 1 | 0 | ⤭ | XOR, != |
| 0 | 1 | 1 | 1 | ⤭ | OR |
| 1 | 0 | 0 | 0 | ⤭ | NOR |
| 1 | 0 | 0 | 1 | ⤭ | XNOR, == |
| 1 | 0 | 1 | 0 | ⤫ | !q |
| 1 | 0 | 1 | 1 | ⤫ | https://en.wikipedia.org/wiki/Converse_implication |
| 1 | 1 | 0 | 0 | ⤫ | !p |
| 1 | 1 | 0 | 1 | ⤫ | https://en.wikipedia.org/wiki/Material_conditional |
| 1 | 1 | 1 | 0 | ⤭ | NAND |
| 1 | 1 | 1 | 1 | ⤭ | true |
Note: Based on https://en.wikipedia.org/wiki/Truth_table#Binary_operations BUT with reordering the rows of the first table for our sort order