1. Symbolic Logic
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2. Pitfalls
This statement is false. vs. This statement is true. Please answer yes/no. Will the next word out of your mouth be "No?" ~ LIAR! Have you lived here all your life? ~ No, not yet. Hippie, you lost a shoe. ~ Oh, no I found one. Russell's paradox- Can you shave everyone in this room who doesn't shave him or herself? If you can, I'll give you $1M.
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3. Aristotelian Logic
Principle of Identity ~ X = X. Principle of excluded middle ~ To be or not to be; true or false Principle of contradiction ~ Propositions cannot be true and false; only true or false.
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4. Propositions p: 2 + 4 = 10; q: 3 + 12 = 15; r: x – 3 = 13
p is false; q is true; and r is not a proposition.
Negation symbol ~; Universal Quantifier
Existential Quantifier
Conjunction ^ AND p ^ q
Truth Values p q p^q p ~p
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5. Symbols
Disjunction v OR p v q p q p v q p => q Implication => implies p => q means p implies q Converse of p => q is q => p Inverse of p => q is ~p => ~q Contrapositive of p => q is ~q => ~p equivalent to p => q
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6. Tautologies
A compound proposition that is true regardless of the truth values of its components. p v ~p p ~p p v ~p
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