1 / 13

2.1 Conditional Statements

2.1 Conditional Statements. Chapter 2: Reasoning and Proof. If –Then Statements. Conditional : another name for an if-then statement. “If you are not completely satisfied, then your money will be refunded.”. Hypothesis : the part following the if.

moses
Download Presentation

2.1 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. 2.1 Conditional Statements Chapter 2: Reasoning and Proof

  2. If –Then Statements Conditional: another name for an if-then statement “If you are not completely satisfied, then your money will be refunded.” Hypothesis: the part following the if Conclusion: the part following the then

  3. Identifying the Hypothesis and Conclusion Identify the hypothesis and the conclusion of this conditional statement: “If today is the first day of fall, then the month is September.” Hypothesis: Conclusion: Today is the first day of fall The month is September

  4. Writing a Conditional Write each sentence as a conditional: • A rectangle has four right angles. • A tiger is an animal. • An integer that ends with 0 is divisible by 5. • A square has four congruent sides. If a figure is a rectangle, then it has four right angles. If something is a tiger, then it is an animal. If an integer ends with 0, then it is divisible by 5. If a figure is a square, then it has four congruent sides.

  5. Truth Value A conditional can have a truth value of true or false. To show that a conditional is true, show that every time the hypothesis is true, the conclusion is also true. To show that a conditional is false, you only need to find one counterexample.

  6. Finding a Counterexample Show that this conditional is false by finding a counterexample: If it is February, then there are only 28 days in the month. Counterexample: There are 29 days in a leap year.

  7. Finding a Counterexample Show that this conditional is false by finding a counterexample: If the name of a state contains the word New, then the state borders an ocean. Counterexample: New Mexico

  8. Using a Venn Diagram Draw a Venn diagram to illustrate this conditional: “If you live in Chicago, then you live in Illinois.” Residents of Illinois Residents of Chicago

  9. Using a Venn Diagram Draw a Venn diagram to illustrate this conditional: “If something is a Cocker Spaniel, then it is a dog.” Dogs Cocker Spaniels

  10. Converse: switches the hypothesis and the conclusion Conditional: If two lines intersect to form right angles, then they are perpendicular. Converse: If two lines are perpendicular, then they intersect to form right angles.

  11. Writing a converse Conditional: If two lines are not parallel and do not intersect, then they are skew. Converse: If two lines are skew, then they are not parallel and do not intersect.

  12. Finding the Truth Value of a Converse Conditional: If a figure is a square, then it has four sides. Converse: If a figure has four sides, then it is a square. *Is this statement true? No, a rectangle also has four sides, so the converse is false. *Look in book, page 70, Summary box for Symbolic Form

  13. Homework Pg 71 2 – 34 even, 64 – 67all

More Related