ch1_2_Propositional Equivalence-part2

ch1_2_Propositional Equivalence-part2 - Example3...

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Unformatted text preview: Example 3 Show that (p q) and(p q) is logically equivalent. (Proof) (p q) (p q) ( p q) (p q) Definition of implication De Morgan 12 Example 4‐1 Show that (p v (P q)) and p q is logically equivalent. (Proof) (p v (P q)) p (P q) by the second De Morgan law p [P q)] p (P v q) (p P) v (p q) F v (p q) p q by the first De Morgan law by the double negation law by the second distributive law by the identity law for F 13 Example 4‐2 Show that (p v (p q)) and p q is logically equivalent. (Using another solution) (p v (P q)) [(p v p) (p v q)] [ T (p v q)] T v (P v q) F v (P v q) F v (p q) p q by distributive law by negation law by De Morgan law T = F by De Morgan law by Identity Law 14 Example 5 At a trial: o Bill says: “Sue is guilty and Fred is innocent.” o Sue says: “If Bill is guilty, then so is Fred.” o Fred says: “I am innocent, but at least one of the others is guilty.” Let b = Bill is innocent, f = Fred is innocent, and s = Sue is innocent Statements are: o ¬s f o ¬b → ¬f o f (¬b ¬s) Can all of their statements be true??? Assignment Due to next lecture 15 ...
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