In: Advanced Math
Using only the rules of SD, derive the following rules of SD+:
a) Disjunctive Syllogism (one case) :
P v Q
~P
b) Commutation: (wedge only) :
P v Q <--> Q v P
c) Implication :
P ⊃ Q <--> Q ⊃ ~P
d) Double Negation
P <--> ~~P
e) DeMorgan
(~(P & Q) <--> ~P v ~Q only)
Use SL sentences rather than metavariables in your derivations. Each direction of replacement rules must be shown (that is, you are proving "equivalence in SD" in these cases)