| a | b | f | ¬∨ | ↛ | ¬b | ↚ | ¬a | ↮ | ¬∧ | ∧ | ↔ | a | ← | b | → | ∨ | t | |||
| 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | |||
| 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | |||
| 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | |||
| 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||
| vz | .. | -- | +- | .- | -+ | -. | 00 | -- | ++ | 00 | +. | +- | .+ | -+ | ++ | .. | ||||
| sx | .. | ff | fw | wf | .. | ww | ww | .. | fw | wf | ff | |||||||||
|
a↔b
= (a→b)∧(b→a) = (a∧b)∨(¬a∧¬b)= (¬a∨b)∧(¬b∨a) a ↮b = (a→¬b)∧(¬b→a)= (a∧¬b)∨(¬a∧b) = (a∨b)∧(¬a∨¬b) |
|
| a∨(b∨c) = (a∨b)∨c | a∧(b∨c) = (a∧b)∨(a∧c) | (a→b)∧(a→c) = a→(b∧c) |
| a∧(b∧c) = (a∧b)∧c | a∨(b∧c) = (a∨b)∧(a∨c) | (a→b)∨(a→c) = a→(b∨c) |
| a∨(b→c) = c∨(b→a) = b→(a∨c) | a∧(b→c) = (a→b)→(a∧c) | (a→c)∧(b→c) = (a∨b)→c |
| (a∧b)→c = a→(b→c) = ¬a∨¬b∨c | (a→b)→c = (a∨c) ∧ (b→c) | (a→c)∨(b→c) = (a∧b)→c |
| (a→b)→(a→c) = a→(b→c) | a∨(b↔c) = (a∨b)↔(a∨c) | a∨(b↮c) = (a∨b)↔(a←c) |
| (a→c)→(b→c) = c∨(b→a) | a∧(b↔c) = (a∧b)↔(a→c) | a∧(b↮c) = (a∧b)↮(a∧c) |
| (a↔b)↔c = a↔(b↔c) = (a↮b)↮c | a→(b↔c) = (a∧b)↔(a∧c) | a→(b↮c) = (a→b)↮(a∧c) |
| (a↔b)↮c = a↔(b↮c) = (a↮b)↔c | a→(b↔c) = (a→b)↔(a→c) | a←(b↔c) = (a∨b)↔(a←c) |
| (a→z)⇒(a∧b)→(z∧b) | (a→z)⇒(a∨b)→(z∨b) | (a→z)⇒(a→b)←(z→b) | (a→z)⇒(a←b)→(z←b) |
| (a←z)⇒(a∧b)←(z∧b) | (a←z)⇒(a∧b)←(z∧b) | (a←z)⇒(a→b)→(z→b) | (a←z)⇒(a←b)←(z←b) |
| a∧b=a∧(b∧a) | a∨b=a∨(b∧¬a) | a→b=a→(b∧a) | a←b=a←(b∧¬a) |
| (a∧b)∨(c∧d) ⇒ (a∨c)∧(b∨d) | (a→b)∧(c→d) ⇒ (a∧c)→(b∧d) |
| (a∨b)∧(c∨d) ⇐ (a∧c)∨(b∧d) | (a→b)∧(c→d) ⇒ (a∨c)→(b∨d) |
| (a→b)∨(c→d) = (a∧c)→(b∨d) |
| a∧f = f | (a∧b)∨a = a | (a↔b)∧a = a∧b | (a∧b)∨¬a =a→b | (a↔b)∧¬a = ¬a∧¬b |
| a∧w = a | (a∨b)∧a = a | (a↔b)∨a = b→a | (a∨b)∧¬a = ¬a∧b | (a↔b)∨¬a = a→b |
| a∨f = a | (a∧b)→a = t | (a↔b)→a = a∨b | (a∧b)→¬a = ¬(a∧b) | (a↔b)→¬a = a→¬b |
| a∨w = w | (a∨b)→a = b→a | a→(a↔b) = a→b | (a∨b)→¬a = ¬a | ¬a→(a↔b) = b→a |
| a→f = ¬a | (a→b)→a = a | a↔(a∧b) = a→b | (a→b)→¬a = ¬(a∧b) | ¬a↔(a∧b) = ¬(a→b) |
| a→w = w | (a→b)→b = a∨b | a↔(a∨b) = b→a | (a→b)→¬b = ¬b | ¬a↔(a∨b) = ¬(b→a) |
| f→a = w | a∧(a→b) = a∧b | a↔(a→b) =a∧b | ¬a∧(a→b) = ¬a | ¬a↔(a→b) =¬(a∧b) |
| w→a = a | a∧(b→a) = a | a↔(b→a) = a∨b | ¬a∧(b→a) = ¬a∧¬b | ¬a↔(b→a) = (¬a∨b) |
| a↔w = a | a∨(a→b) = t | ¬a∨(a→b) = a→b | ||
| a↔f = ¬a | a∨(b→a) = b→a | ¬a∨(b→a) = ¬a | a∧¬a = f | |
| a∧a = a | a→(a∧b) = a→b | ¬a→(a∧b) = a | a∨¬a = t | |
| a∨a = a | a→(a∨b) = t | ¬a→(a∨b) = a∨b | a→¬a = ¬a | |
| a→a = w | a→(a→b) = a→b | ¬a→(a→b) = t | ¬a→a = a | |
| a↔a = w | a→(b→a) = t | ¬¬a=a | ¬a→(b→a) = b→a | a↔¬a = f |