1 / 17

2-3 Conditional Statements

2-3 Conditional Statements. Ms. Andrejko. Real Life. If you would like to speak to a representative press 0 now. Vocabulary . Conditional Statement- a statement that can be written in if-then form If-then statement- is of the form if p , then q

palila
Download Presentation

2-3 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. 2-3 Conditional Statements Ms. Andrejko

  2. Real Life If you would like to speak to a representative press 0 now

  3. Vocabulary • Conditional Statement- a statement that can be written in if-then form • If-then statement- is of the form if p, then q • Hypothesis- the phrase immediately following the word if • Conclusion- the phrase immediately following the word then • Related Conditionals- other statements that are based on a given conditional statement • Logically equivalent- Statements with the same truth values

  4. Notation pq= if p, then q p= hypothesis q= conclusion

  5. Conditional Truth Table

  6. Examples • Identify the hypothesis and conclusion: • If 3x+4=-5, then x=-3 • If you take a class in television broadcasting, then you will film a sporting event Hypothesis: 3x+4=-5 Conclusion: x=-3 Hypothesis: Take a class in television broadcasting Conclusion: Film a sporting event

  7. Practice • Identify the hypothesis and conclusion: • If you purchase a computer and don’t like it, then you can return it within 30 days. • If x+8 = 4, then x= - 4 Hypothesis: purchase a computer and don’t like it Conclusion: return it within 30 days Hypothesis: x+8=4 Conclusion: x= -4

  8. Examples • Write each statement in if-then form: • Those who do not remember the past are condemned to repeat it. • Adjacent angles share a common vertex and a common side IF you do not remember the past, THEN you are condemned to repeat it. IF 2 angles are adjacent, THEN they share a common vertex and common side.

  9. Practice • Write each statement in if-then form: • A polygon with four sides is a quadrilateral. • An acute angle has a measure less than 90. IF a polygon has four sides, THEN it is a quadrilateral IF an angle is acute, THEN its measure is less than 90.

  10. Examples • Determine the truth vale of the following conditionals: • If a and b are negative, then a + b is also negative. • If you have five dollars, then you have five one-dollar bills. T  T = T T  F = F Counterexample: you have 1, $5 bill.

  11. Practice • Determine the truth vale of the following conditionals: • If two angles are supplementary, then one of the angles is acute. • If I roll two six-sided dice and sum of the numbers is 11, then one die must be a five. T  F = F Counterexample: 90° and 90° - neither are acute T  T = T 5+6 = 11

  12. FOLDABLE INSIDE CONDITIONAL TAB Hypothesis Conclusion If-Then Statement

  13. Vocabulary qp • Converse- formed by exchanging the hypothesis and conclusion • Inverse- formed by negating the hypothesis and conclusion of the conditional • Contrapositive- formed by negating the hypothesis and conclusion of the converse ~p ~q ~q ~p

  14. IMPORTANT NOTE **** NOTE: • The conditional and it’s contrapositiveare logically equivalent • The converse and inverse are logically equivalent

  15. Examples • Write the converse, inverse, and contrapositive of each statement: • If 89 is divisible by 2, then 89 is an even number • If an animal is a lion, then it is a cat that can roar Converse: If 89 is an even number, then 89 is divisible by 2. Inverse: If 89 is not an even number, then 89 is not divisible by 2. Contrapositive: If 89 is not an even number, then 89 is not divisible by 2. Converse: If an animal is a cat that can roar, then it is a lion. Inverse: If an animal is not a lion, then it is not a cat that can roar. Contrapositive: If an animal is not a cat that can roar, then it is not a lion.

  16. Examples • Write the converse, inverse, and contrapositive of each statement: • If you are 15 years old, then you are eligible to drive. • If the temperature is freezing, then precipitation falls as snow. Converse: If you are eligible to drive, then you are 15 years old. Inverse: If you are not 15 years old, then you are not eligible to drive. Contrapositive: If you are not eligible to drive, then you are not 15 years old. Converse: If precipitation falls as snow, then the temperature is freezing. Inverse: If the temperature isn’t freezing, then the precipitation does not fall as snow. Contrapositive: If precipitation doesn’t fall as snow, then the temperature isn’t freezing.

  17. FOLDABLE INSIDE CONDITIONAL TAB Converse Inverse Contrapositive

More Related