Week 1.6 Homework Packet

Transcription

1 Name: Week 1.6 Homework Packet 1. For the given statement, write the conditional statement, the converse, the inverse, and the contrapositive. Tell if each is true or false. If it is false, give a counterexample. a. Ants are insects b. 3x + 10 = 16, because x = Decide whether the statement is true or false. If true, tell me why. If false, provide a counterexample. a. If a polygon has five sides, then it is a regular pentagon. (First tell me what regular means!) b. If m A is 85º, then the measure of the complement of A is 5º. (First tell me what complement means!) c. Supplementary angles are always linear pairs. (First tell me what supplementary and linear pair means!) 1

2 3. Decide whether each statement about the diagram is true. Explain your answer using the definitions you have learned. a. b. c. 4. Rewrite the definition as a biconditional statement. a. An angle with a measure between 90º and 180º is called obtuse. b. Coplanar points are points that lie in the same plane. c. Two angles whose sum is 90º are called complementary angles. 5. Write the converse of each true statement. Tell whether the converse is true or false. If true, explain. If false, give a counterexample. a. If x > 4, then x > 0. b. If x < 6, then x > -6 2

3 6. Determine if the biconditional statement is true or false. If false, provide a counterexample. a. b. 7. How can you show that the statement, If you play a sport, then you wear a helmet. is false? Explain. 8. Using the Law of Detachment, make a valid conclusion. a. If the measure of an angle is 90º, then it is a right angle. The measure of A is 90º. b. If x > 12, then x < -12. The value of x is 15. c. If a book is a biography, then it is nonfiction. You are reading a biography. 9. Using the Law of Syllogism, write the statement that follows from the pair of given statements. a. If a rectangle has four equal side lengths, then it is a square. If a polygon is a square, then it is a regular polygon. b. If y > 0, then 2y > 0. If 2y > 0, then 2y

4 10. What is the error in this argument: If two angles are a linear pair, then they are supplementary. Angles C and D are supplementary, so the angles are a linear pair. 11. Select the word (s) that make (s) the conclusion true. a. Mesa Verde National Park is in Colorado. Sally vacationed in Colorado. So, Sally (must have, may have, or never) visited Mesa Verde National Park. b. The cliff dwellings in Mesa Verde National Park are accessible to visitors only when accompanied by a park ranger. Jennifer is at a cliff dwelling in Mesa Verde National Park. So, Jennifer (is, may be, is not) with a park ranger. 12. The rule at school is that you must attend all of your classes in order to participate in sports after school. You went to all of your classes, therefore you played in a football game after school on Friday Is this inductive or deductive reasoning? Why? 13. For the past 5 years, your neighbor goes on vacation every July 4 th and asks you to feed her dog. You conclude that you will be asked to feed her dog on the next July 4 th. Is this inductive or deductive reasoning? Why? 14. 4

5 15. Use the diagram to determine if the statements are true or false. Underline the hypothesis once and the conclusion twice. 16. If you can see the magic in a fairy tale, you can face the future. Danielle Steel, novelist 17. If somebody throws a brick at me, I can catch it and throw it back. Harry S Truman 18. If you can accept defeat and open your pay envelope without feeling guilty, you re stealing. George Allen, former NFL coach 19. If my fans think that I can do everything I say I can do, then they re crazier than I am. Muhammad Ali 20. if I could paint that flower in a huge scale, you could not ignore its beauty. Georgia O Keeffe, artist 5

6 Advertisements 21. Al sees an ad that states, You want to look good at the beach this summer. Join GoodFit Health Club. Al figures, I am going to join GoodFit Health Club, so that I will look good at the beach. a. Write the statement in the ad as a conditional statement. b. Write Al s statement as a conditional statement. c. What is wrong with Al s logic? 22. Read the advertisement at the right. What conditional statement is implied by the ad? 6

7 Logic Notation 23. Let statements p, q, and r be as follows: p: A figure is a square. q: A figure has four congruent angles. r: A figure has four congruent sides. Write the words for the symbolic statement shown. Determine the truth value of the statement. If it is false, provide a counterexample. a. p q b. q p c. r q d. ( q and r) p 24. Is each statement below a good definition? If not, why? (Reminder: what must be true for a definition to be good??) d. A cat is an animal with whiskers. e. A segment is part of a line. f. A square is a figure with two pairs of parallel lines. g. A dog is a good pet. 7

8 25. Write the two statements that form the biconditional statement. h. An integer is divisible by 100 if and only if its last two digits are zeros. Use the Law of Syllogism to draw a conclusion. 26. In a band, Amy, Bob, and Carla are the drummer, guitarist, and keyboard player. Carla and the drummer wear different colored shirts. The keyboard player is older than Bob. Amy, the youngest band member, lives next door to the guitarist. Use the clues to find the instrument each one plays. 27. If an animal is a red wolf, then its scientific name is Canis rufus. If an animal is named Canis rufus, then it is endangered. 28. If two planes intersect, then they intersect in a line. If two planes are not parallel, then they intersect. 29. If you are studying biology, then you are studying a science. If you are studying botany, then you are studying biology. 8