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03h - Discrete Mathematics Propositional Logic II 3-2...

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Introduction Propositional Logic II Discrete Mathematics Andrei Bulatov 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 Discrete Mathematics – Propositional Logic 3-3 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” Discrete Mathematics – Propositional Logic 3-4 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” Discrete Mathematics – Propositional Logic II 3-5 An Example Construct the truth table of the following compound statement p (q ∨ ¬ p) Discrete Mathematics – Propositional Logic II 3-6
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