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