1 / 23

Unit 3 Analyze Conditional Statements

Unit 3 Analyze Conditional Statements. Logical statement written in if-then form. If p, then q. p  q. Statement following the “if”. “p” part. Statement following the “then”. “q” part. Assuming “p” is true, the “q” HAS to happen.

amarin
Download Presentation

Unit 3 Analyze Conditional Statements

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unit 3 Analyze Conditional Statements

  2. Logical statement written in if-then form. If p, then q. pq Statement following the “if” “p” part Statement following the “then” “q” part

  3. Assuming “p” is true, the “q” HAS to happen Assuming “p” is true, the “q” might not happen. You only need ONE example to prove a statement false. One example that proves a statement is false. When p is true, but q is false.

  4. Flip the hypothesis and conclusion If p, then q becomes If q, then p qp Negate the hypothesis and conclusion If p, then q becomes If not p, then not q ~p ~q

  5. Negate the hypothesis and conclusion of the converse If p, then q becomes If not q, then not p ~q ~p Equivalent to the original statement.

  6. Original and converse of a statement are true. p if and only if q p iff q p q AND q  p pq

  7. 1. State the hypothesis and conclusion of the following: a. If a student studies for a test, then they will get an A in the class. conclusion hypothesis

  8. 1. State the hypothesis and conclusion of the following: b. If you are a football player, then you are an athlete. conclusion hypothesis

  9. 1. State the hypothesis and conclusion of the following: c. If x = 3, then x2 = 9. hypothesis conclusion

  10. 2. Rewrite the statement in if-then form. Then write the converse, the inverse, and the contrapositive. A car runs when there is gas in the tank. If-then: If a car is running, then there is gas in the tank. Converse: If there is gas in the tank, then the car is running. Inverse: If the car isn’t running, then there isn’t gas in the tank. Contra: If there isn’t gas in the tank, then the car isn’t running.

  11. 2. Rewrite the statement in if-then form. Then write the converse, the inverse, and the contrapositive. All triangles have three sides. If-then: If a polygon is a triangle, then it has 3 sides. Converse: If a polygon has 3 sides, then it is a triangle. Inverse: If a polygon isn’t a triangle, then it doesn’t have 3 sides. Contra: If a polygon doesn’t have 3 sides, then it isn’t a triangle.

  12. 3. Rewrite the definition as a biconditional statement. Two angles are complementary angles when the sum of their measures is 90° Two angles are complementary angles IFF their sum measures 90°

  13. 3. Rewrite the definition as a biconditional statement. Equilateral polygons have all of their sides congruent. A polygon is equilateral IFF all of the sides are congruent

  14. 4. Determine if the if-then statement is true or false. If false, provide a counterexample. a. If you drive a mustang, then it is red. False, You drive a mustang that is black.

  15. 6. Determine if the if-then statement is true or false. If false, provide a counterexample. b. If m2 = 90°, then it is a right angle. True

  16. 6. Determine if the if-then statement is true or false. If false, provide a counterexample. c. If A is obtuse, then it measures 155° False, An obtuse angle that is 100°

  17. 6. Determine if the if-then statement is true or false. If false, provide a counterexample. d. If you stay after school, then you go to math tutorial. False, You stay after school for sports practice

  18. 7. Decide whether each statement about the diagram is true. Explain your answer. mAEB = 90° B False, A C E No Box! D

  19. 7. Decide whether each statement about the diagram is true. Explain your answer. AE + EC = 180° B False, A C E Segments aren’t measured in degrees! D

  20. 7. Decide whether each statement about the diagram is true. Explain your answer. AEDBEC B True, A C E Vertical Angles D

  21. THE FIRE-FISH STORY “If there is a fire, then a fish dies” You are to write a creative story consisting entirely of conditional statements. The first statement should be of the form: “If there is a storm, then A.” The second statement should be of the form: “If A, then B.” The hypothesis of each statement must be the conclusion of the previous statement. The story must be out of at least 5 conditional statements, ending with “If D, then Mr. Keeney orders pizza for the class.”

  22. If there is a storm, then _________________________________. If ________________, then ………………………………… If …………………………., then ***************************************. If *******************************, then xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx. If xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx, then Mr. Keeney buys pizza for the class.

  23. HW Problem # 19 An angle measures between 90° and 180° IFF it is obtuse

More Related