Propositional Calculus Solution Outline

Propositional Calculus Solution Outline - (all...

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Propositional Calculus Solution Outline Problem 1: (a) E = Relation is an Equivalence Relation R = Relation is Reflexive S = Relation is Symmetric T = Relation is Transitive E <==> (R and S and T) (b) C = person has courage S = person has skill M = person can climb mountain (C and S) => M (c) C = man who campaigns hard E = he probably will be elected C => E Problem 2: (a) if he is sick then he needs a doctor, and if he has an accident then he needs a lawyer (b) He needs a lawyer and a doctor if and only if he is sick and injured (c) If he is neither sick nor injured then he does not need a doctor Problem 3: Hint: A unless B stands for: (not A => B) P = congress refuses to enact new laws Q = strike will not be over R = president of firm resigns S = the strike lasts for more than a year F1 : (P => ( not Q => (R and S) ) F2: (not P and Q) => S Now draw the truth table of F1 => F2, and check if it is valid
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Unformatted text preview: (all interpretations are models), inconsistent (no interpretation is a model) or satisfiable (at least one intrpretation is a model). Note: Model of a formula G is an interpretation in which G is true. Problem 4: Assume same encoding as problem 3: F1: (P =&gt; (not Q =&gt; (R and S)) F2: P F3: not Q F4: not R theorem to prove: S Show that S is a logical consequence of formulas F1, F2, F3 and F4. To do this either show that (F1 and F2 and F3 and F4) =&gt; G is a tautology or show that F1 and F2 and F3 and F4 and not G is inconsistent or show that every model of F1 and F2 and F3 and F4 is a model of G. Problem 5: G = Tom is a good student P = Tom's father supports him S = Tom is smart F1: G =&gt; (P and S) F2: G =&gt; P Show F1 =&gt; F2 is a valid formula (i.e., it is a tautology)...
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Propositional Calculus Solution Outline - (all...

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