Editing Mathematical Logic (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'Logical Evaluation' (Truth Tables):'''
<syntaxhighlight lang="python">
def evaluate_implication(p_true, q_true):
    """
    Implication: P -> Q (If P, then Q)
    Only False if P is True and Q is False.
    """
    if p_true and not q_true:
        return False
    return True

# Scenario: 'If you are a bird (P), you can fly (Q)'
# Testing a Penguin (P=True, Q=False)
print(f"Is 'Bird -> Fly' valid for a Penguin? {evaluate_implication(True, False)}")
# Logic helps us find the 'Counter-examples' that 
# break our theories.
</syntaxhighlight>

; Logic Milestones
: '''Principia Mathematica (Russell/Whitehead)''' → A massive attempt to derive all of math from pure logic (later shown to be incomplete by Gödel).
: '''Boolean Algebra''' → The logic of 0 and 1 that powers every computer chip in the world.
: '''The Halting Problem''' → Alan Turing's proof that there are some things a computer can never figure out.
: '''Fuzzy Logic''' → A type of logic where statements can be "partially true" (e.g., 0.7 true), used in AI and smart appliances.
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