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03 - Propositional Introduction Logic II Discrete...

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Introduction Propositional Logic II Discrete Mathematics Andrei Bulatov
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Discrete Mathematics – Propositional Logic II 3-2 Previous Lecture Statements, primitive and compound Logic connectives: Truth tables square4 negation ¬ square4 conjunction square4 disjunction square4 exclusive or square4 implication square4 biconditional
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Example `You can access the Internet from campus if you are a computer science major or if you are not a freshman.’ p - `you can access the Internet from campus’ q - `you are a computer science major’ r - `you are a freshman’ Discrete Mathematics – Propositional Logic II 3-3
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Discrete Mathematics – Propositional Logic 3-4 Tautologies Tautology is a compound statement (formula) that is true for all combinations of truth values of its propositional variables (p q) (q p) p q (p q) (q p) 0 0 1 0 1 1 1 0 1 1 1 1 “To be or not to be”
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Discrete Mathematics – Propositional Logic 3-5 Contradictions Contradiction is a compound statement (formula) that is false for all combinations of truth values of its propositional variables (p q) (p ⊕ ¬ q) p q (p q) (p ⊕ ¬ q) 0 0 0 0 1 0 1 0 0 1 1 0 “Black is white and black is not white”
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Discrete Mathematics – Propositional Logic II 3-6 An Example Construct the truth table of the following compound statement p (q ∨ ¬ p)
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