3 ms·
I'll add that the significance of the formula is it's similar to a*b + a*c = a*(b + c) which you ought to remember from school as "factoring/factorization".
by jkabrg 8y ago
I'll add that the significance of the formula is it's similar to
a*b + a*c = a*(b + c)
which you ought to remember from school as "factoring/factorization". Except in this case, " * " is replaced with "V", and "+" is replaced with "->". In mathematics, you call that a "distributive law". Some more examples are
a^c * b^c = (a*b)^c
p/\q V p/\r = p/\(q V r)
(pVq) /\ (pVr) = pV(q /\ r)
- Twisol 8y agoWhile 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.