Editing Propositional Logic (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
Propositional logic is understood through '''Structure''' and '''Certainty'''.

'''1. The Logic of "If... Then" (Implication)''':
This is the most misunderstood part of logic.
* In logic, "If P then Q" is only **FALSE** if P is true but Q is false.
* If P is false, the whole statement is "Vacuously True."
* For example: "If I am a billionaire, I will buy you a car." If I am *not* a billionaire, I haven't lied! The statement is still technically "True" because the condition wasn't met.

'''2. Truth Tables (The Map of Truth)''':
A truth table allows us to "Calculate" the truth of any statement.
* If you have two inputs (P and Q), there are 4 possible worlds: (T,T), (T,F), (F,T), (F,F).
* By filling in the table, we can prove that two different sentences mean exactly the same thing (Logical Equivalence).
* For example, "If it rains, I get wet" is the same as "Either it doesn't rain, or I get wet."

'''3. De Morgan’s Laws''':
A fundamental rule of logic:
* "NOT (P AND Q)" is the same as "(NOT P) OR (NOT Q)."
* For example: "It is not the case that I am both rich AND happy" means "I am either not rich OR I am not happy."

'''The 'Law of the Excluded Middle'''': The core rule of classical logic: a statement is either True or False. There is no "Maybe" or "Half-true." (While some "Fuzzy Logic" systems challenge this, most of math and computer science is built on this "Yes/No" binary).
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