COT3100Exam1Review - Outline of COT 3100 material for first...

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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 F. Inclusion-Exclusion Principle Reading in texbook: 2.1 – 2.5, 3.1 – 3.3
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1) In a language survey of students it is found that 80 students know English, 60 know French, 50 know German, 30 know English and French, 20 know French and German, 15 know English and German and 10 students know all three languages. How many students know a) at least one language? b) English only? c) French and one but not both out of English and German? d) at least two languages? Use the inclusion-exclusion principle to handle each of these questions. | A B C| = |A| + |B| + |C| | A B | | B C | | A C | + | A B C |. Let A = students who speak English, B = students who speak French, and C = students that speak German | A B C| = 80 + 60 + 50 – 30 – 20 – 15 + 10 = 135 total
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COT3100Exam1Review - Outline of COT 3100 material for first...

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