There are two ways in which we can use all real numbers between $0$ and $1$ to represent Boolean expressions that satisfy De Morgan's Laws. What are they?
I have found the first way. For propositions $p, q \in [0, 1]$, define $p \wedge q = \text{min}(p, q)$ and $p \vee q = \text{max}(p, q)$, and define $\neg p = 1 - p$.
These satisfy De Morgan's Laws.
I can't find the second one. Can someone please help me? I've seen it before, and I remember that it only used algebra (multiplication, addition, subtraction). They didn't have any special functions (like max/min). Can someone please help me recall them?
Define
$ p ∧ q := p \times q $
$ ¬p := 1 - p $
then you can define disjunction to make the DeMorgan laws hold, and you get
$ p ∨ q := 1 - ( (1 - p) \times (1 - q) ) $