3 ms·
While you're absolutely right that this is a kind of distributivity, conventionally + is related to "or", * to "and", and ^ to "implies". So the theorem as give
by Twisol 8y ago
While you're absolutely right that this is a kind of distributivity, conventionally + is related to "or", * to "and", and ^ to "implies". So the theorem as given would be rendered as something more like "(p + r)^(p + q) implies (p + r^q)".
- pofilat 8y agoThat's interesting.... + and * theorems correspond between logic and arithmetic, but taking ^ as implication generates theorems that are true in logic but not in arithmetic. (The truth table of implication is clearly different from binary exxponentiation)
- Twisol 8y agoIs it? I checked before commenting (because I also wanted to make sure the arithmetic analogy actually held): irb(main):001:0> 0**0 => 1 irb(main):002:0> 0**1 => 0 irb(main):003:0> 1**0 => 1 irb(main):004:0> 1**1 => 1 Notice that `p -> q` becomes `q^p`, i.e. the operands swap position.