exam1sol - Honors Introduction to Discrete Structures COT...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 = _____________________________________________________________...
View Full Document

{[ snackBarMessage ]}

Page1 / 6

exam1sol - Honors Introduction to Discrete Structures COT...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online