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# Sheet11 - decomposed into prime factors(See textbook 4.2...

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McMaster University Department of Computing and Software Dr. W. Kahl COMP SCI 1FC3 Exercise Sheet 11 COMP SCI 1FC3 — Mathematics for Computing 7 April 2009 Exercise 11.1 — Equivalence Reasoning in Propositional Logic Using the basic propositional logic equivalences (and documenting their use), derive the following equiv- alence: ( ( p q ) ∧ ( p r ) ) ( p → ( q r ) ) Exercise 11.2 — Quantifiers (5%of Final 2008) Explain why the order of quantifiers and in a formula is important. Use an explicit example to illustrate your point. Exercise 11.3 — Strong Induction (8%of Final 2008) State the principle of Strong Induction. Use strong induction to prove that all positive integers can be
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Unformatted text preview: decomposed into prime factors. (See textbook 4.2 Example 2 pp. 285–286.) Exercise 11.4 — Syntax Trees (5%of Final 2008) Draw the tree that corresponds to the following expression: (( a-b ) / 3)*(5+ (1 /a )) . Give the post-Fx (or reverse Polish notation) version of that expression. Exercise 11.4 — Graphs Strongly-connected components : Textbook 9.4 Exercises 11–16 (pp. 630–631) Shortest paths : Textbook 9.6 Exercises 1–14 (pp. 655–656)...
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