COT3100Exam1ReviewSpr08

# COT3100Exam1ReviewSpr08 - Outline of COT 3100 material for...

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Outline of COT 3100 material for first exam I. Logic A. Symbols( , , and ¬ ) B. Truth Tables C. Logic Laws D. Methods of showing equality of logical expressions E. Implication Rules F. Contrapositive of a stmt. G. Quantifiers II. Sets A. Symbols( , , , , ¬ , , and ) B. Set Laws C. Membership Table D. Proof Techniques for if-then statements i. direct proof ii. proof of contrapositive iii. proof by contradiction E. How to Disprove an if-then statement Reading in texbook: 2.1 – 2.5, 3.1 – 3.2

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1) Show that the following expression is a tautology: ( (p r) ( (q r) p) ) ¬ ( ( ¬ (p q) ) p ) ( (p r) ( (q r) p) ) ¬ ( ( ¬ (p q) ) p ) ( (p r) ( (q r) p) ) ¬¬ ( p q) ¬ p (De Morgans) ( (p r) ( (q r) p) ) ( p q) ¬ p (Double Negation) ( ¬ p p) ( (p r) (q r) (p q)) (Comm/Assoc or) T ( (p r) (q r) (p q)) (Inverse Law) T (Domination Law) 2) Given the following premises: p p q (q r) s Show that s is true. 1. p (Premise) 2. p q (Premise) 3. q (1+2+Modus Ponens) 4. q r (3+Disjunctive Amplification) 5. q r s (Premise) 6. s (4+5+Modus Ponens)
3) Consider the following three statements: p(x): x 2 – 8x + 15 = 0 q(x): x is odd r(x): x > 0 Which of the following is true?

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