# exam1sol - Honors Introduction to Discrete Structures COT...

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Unformatted text preview: Honors Introduction to Discrete Structures COT 3100H Exam #1: Logic, Sets Date: 1/31/08 Solutions 1) (10 pts) Complete the following truth table. Please designate expressions for the intermediate columns in the table. ) ( p r ¬ ∧ p q r ) ( q p ¬ ∧ ) ( p r ¬ ∧ ) ( p r ¬ ∧ ¬ ) ( ) ( p r q p ¬ ∧ ¬ ∨ ¬ ∧ F F F F F T T F F T F T F F F T F F F T T F T T F T F F T F F T F T T T F T T F T T T T F F F T T T T T F F T T 2) (10 pts) Use the laws of logic to show that r q r p r p ∨ ∨ ∧ ∧ ∧ ¬ )) ) (( ) (( is a tautology. r r p r q r p r p ∨ ∧ ¬ ↔ ∨ ∨ ∧ ∧ ∧ ¬ ) ( )) ) (( ) (( , Absorption r r p ∨ ¬ ∨ ¬ ↔ ) ( , DeMorgan's ) ( r r p ∨ ¬ ∨ ¬ ↔ , Associative T p ∨ ¬ ↔ , Inverse T ↔ , Domination 3) (10 pts) Use the rules of implication to prove the following argument: ) ( r q p → → s p ∨ q t → s ¬----------------- t r ¬ → ¬ ∴ 1) s p ∨ Premise 2) s ¬ Premise 3) p Disjunctive Syllogism (1+2) 4) ) ( r q p → → Premise 5) r q → Modus Ponens (3+4) 6) q t → Premise 7) r t → Law of Syllogism (6+5) 8) t r ¬ → ¬ ∴ Contrapositive 4) (10 pts) Give examples of statements p, q, r, s and t for the question above that would exemplify a typical argument/proof that someone would make in real life. (Note: I get to judge if the example is typical enough!) p = _____________________________________________________________ q = _____________________________________________________________ r = _____________________________________________________________...
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exam1sol - Honors Introduction to Discrete Structures COT...

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