Simple tutorial on Propositional Logic

A very simple tutorial explaining Propositional Logic short-hand to everyone that knows Aristotle’s Syllogisms. I am pretty sure that this is all there is to Propositional Logic. If I missed anything please let me know.

Aristotle Syllogism (slightly enhanced):
…..Premise (a) “It is raining outside.”
…..Premise (b) “You go outside unprotected from the rain.”
Conclusion (c) “You get wet.”

Partial translation to Propositional Logic:
if (a) and (b) then (c)

Full translation to Propositional Logic:
(a ∧ b) → c

Propositional Logic Symbols and their English meanings
P …………. P is true
~P ……….. P is not true
P ∧ P ……. P and Q are both true
P ∨ Q ……. either P or Q (or both) are true
P → Q ….. if P is true then Q is true
…………….. if Q is false then P is false
…………….. if P is false then (Q  ∨ ~Q)

If you understand the above then you know your P’s and Q’s