04h - Discrete Mathematics Laws of Logic 4-2 Previous...

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Introduction Laws of Logic Discrete Mathematics Andrei Bulatov Discrete Mathematics – Laws of Logic 4-2 Previous Lecture Truth tables Tautologies and contradictions Logic equivalences Discrete Mathematics – Laws of Logic 4-3 Logic Equivalences Compound statements Φ and Ψ are said to be logically equivalent if the statement Φ is true (false) if and only if Ψ is true (respectively, false) or The truth tables of Φ and Ψ are equal or For any choice of truth values of the primitive statements (propositional variables) of Φ and Ψ , formulas Φ and Ψ have the same truth value If Φ and Ψ are logically equivalent, we write Φ ⇔ Ψ Discrete Mathematics – Laws of Logic 4-4 Example Equivalences Implication and its contrapositive p q p q 0 0 1 0 1 1 1 0 0 1 1 1 ¬ q → ¬ p 1 1 0 1 All tautologies are equivalent to T All contradictions are equivalent to F Discrete Mathematics – Laws of Logic 4-5 Laws of Logic Double negation ¬¬ p p p ¬ p 0 1 1 0 ¬¬ p 0 1 Discrete Mathematics – Laws of Logic 4-6 Laws of Logic
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04h - Discrete Mathematics Laws of Logic 4-2 Previous...

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