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Download Proofs_A4_Review - Kelvin-2011-2012-Sem02
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A4 Logic and Reasoning – Review Mr. Nguyen Grade 11 Applied Math Kelvin High School Part I: Reasoning with Evidence 1. Andy, Bonnie, Candice, and Darlene are standing in line to buy ice cream. Determine the order in which they are lined up, using these clues: Candice is between Andy and Bonnie Darlene is next to Andy Bonnie is not first Part II: Inductive Reasoning 2. Frank tosses a coin five times, and each time it comes up tails. He makes the following conjecture: the coin will come up tails on every toss. Is his conjecture reasonable? Explain. 3. Charles studied the diagonals of the parallelograms below to look for patterns. Make a conjecture about the diagonals of parallelograms. What evidence supports your conjecture? Part III: Counter examples 4. What is a counterexample? Explain why counterexamples are useful. 5. Vince claims that the perimeter of a pentagon with natural number dimensions will always be an odd number. Search for a counterexample to his claim. 6. Harry claims that if opposite sides of a quadrilateral are the same length, the quadrilateral is a rectangle. Do you agree or disagree? Justify your decision 7. Sadie claims that the difference between any two positive integers is always a positive integer. Do you agree or disagree? Justify your decision. A4 Logic and Reasoning – Review Mr. Nguyen Grade 11 Applied Math Kelvin High School Part IV: Deductive Reasoning 8. Complete the conclusion for the following deductive argument: If an integer is an even number, then its square is also even. Six is an even number, therefore… 9. If you are playing this game of tic-tac-toe, you can use a strategy that guarantees you will win the game. Explain what this strategy is. 10. The rules for the game of “15” are given below: The cards are placed on a table between two players Players take turns choosing a card (any card they like) The winner is the first player to have three cards that add to 15. a) Is it possible to win the game in three moves? b) Devise a winning strategy by using deductive reasoning. Explain why your strategy works.
