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Lecture4

# Lecture4 - 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 Why Logic Equivalences To simplify compound statements ``If you are a computer science major or a freshman and you are not a computer science major or you are granted access to the Internet, then you are a freshman or have access to the Internet’’ To convert complicated compound statements to certain `normal form’ that is easier to handle Conjunctive Normal Form CNF Discrete Mathematics – Laws of Logic 4-5 Example Equivalences

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