Unit 3 Analyze Conditional Statements Conditional Statement Hypothesis

  • Slides: 23
Download presentation
Unit 3 Analyze Conditional Statements

Unit 3 Analyze Conditional Statements

Conditional Statement Hypothesis Conclusion Logical statement written in ifthen form. If p, then q.

Conditional Statement Hypothesis Conclusion Logical statement written in ifthen form. If p, then q. p q Statement following the “if” “p” part Statement following the “then” “q” part

True Statement Assuming “p” is true, the “q” HAS to happen Assuming “p” is

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

Converse Inverse Flip the hypothesis and conclusion If p, then q becomes If q,

Converse Inverse 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

Contrapositive Negate the hypothesis and conclusion of the converse If p, then q becomes

Contrapositive 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.

Biconditional statement Original and converse of a statement are true. p if and only

Biconditional statement Original and converse of a statement are true. p if and only if q p iff q p q AND q p p q

1. State the hypothesis and conclusion of the following: a. If a student studies

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. hypothesis conclusion

1. State the hypothesis and conclusion of the following: b. If you are a

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

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

1. State the hypothesis and conclusion of the following: c. If x = 3, then x 2 = 9. hypothesis conclusion

2. Rewrite the statement in if-then form. Then write the converse, the inverse, and

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.

2. Rewrite the statement in if-then form. Then write the converse, the inverse, and

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.

3. Rewrite the definition as a biconditional statement. Two angles are complementary angles when

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°

3. Rewrite the definition as a biconditional statement. Equilateral polygons have all of their

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

4. Determine if the if-then statement is true or false. If false, provide a

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.

6. Determine if the if-then statement is true or false. If false, provide a

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

6. Determine if the if-then statement is true or false. If false, provide a

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°

6. Determine if the if-then statement is true or false. If false, provide a

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

7. Decide whether each statement about the diagram is true. Explain your answer. m

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

7. Decide whether each statement about the diagram is true. Explain your answer. AE

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

7. Decide whether each statement about the diagram is true. Explain your answer. AED

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

THE FIRE-FISH STORY “If there is a fire, then a fish dies” You are

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 The hypothesis of each statement must form: “If A, then B. ” 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. ”

If there is a storm, then _________________. If ________, then ………………… If ……………. ,

If there is a storm, then _________________. If ________, then ………………… If ……………. , then ********************. If ****************, then xxxxxxxxxxxxxxxxxxxx. If xxxxxxxxxxxxxxxx, then Mr. Keeney buys pizza for the class.

HW Problem LT 3. 3 Page # Assignment Due 82 -85 1 -15 odd,

HW Problem LT 3. 3 Page # Assignment Due 82 -85 1 -15 odd, 16 -18, 19 -25 odd Storm-Pizza Story # 19 An angle measures between 90° and 180° IFF it is obtuse

Conditional Statements Conditional Statements A CONDITIONAL STATEMENT isConditional Statements Conditional Statements A CONDITIONAL STATEMENT is
2 1 Conditional Statements Conditional Statement Conditional statement2 1 Conditional Statements Conditional Statement Conditional statement
Nested conditional statements Nested conditional statements A conditionalNested conditional statements Nested conditional statements A conditional
CONDITIONAL STATEMENTS Section 2 3 Conditional Statements ConditionalCONDITIONAL STATEMENTS Section 2 3 Conditional Statements Conditional
Analyze Conditional Statements Chapter 2 2 Conditional StatementAnalyze Conditional Statements Chapter 2 2 Conditional Statement
Conditional Statements and Conditional Statements Biconditional Statements WarmConditional Statements and Conditional Statements Biconditional Statements Warm
Conditional Statements Conditional Statements Ifthen statements are calledConditional Statements Conditional Statements Ifthen statements are called
Conditional Statements 1 Conditional Statement Definition A conditionalConditional Statements 1 Conditional Statement Definition A conditional
Lesson Conditional Statements Conditional Statement Defn A conditionalLesson Conditional Statements Conditional Statement Defn A conditional
Lesson Conditional Statements Conditional Statement Defn A conditionalLesson Conditional Statements Conditional Statement Defn A conditional
Conditional Statements Switch Statements Why another conditional statementConditional Statements Switch Statements Why another conditional statement
Conditional Statements Vocabulary Conditional Statement A logical statementConditional Statements Vocabulary Conditional Statement A logical statement
Related Conditionals Conditional Statements Conditional Statement A statementRelated Conditionals Conditional Statements Conditional Statement A statement
2 2 Conditional Statements Conditional Statement A statement2 2 Conditional Statements Conditional Statement A statement
Hypothesis and Hypothesis Testing HYPOTHESIS A statement aboutHypothesis and Hypothesis Testing HYPOTHESIS A statement about
Hypothesis and Hypothesis Testing HYPOTHESIS A statement aboutHypothesis and Hypothesis Testing HYPOTHESIS A statement about
Hypothesis and Hypothesis Testing HYPOTHESIS A statement aboutHypothesis and Hypothesis Testing HYPOTHESIS A statement about
Conditional Statements Definitions Conditionals Hypothesis Conclusions A conditionalConditional Statements Definitions Conditionals Hypothesis Conclusions A conditional
2 2 Analyze Conditional Statements n Definitions conditional2 2 Analyze Conditional Statements n Definitions conditional
Geometry 2 2 Analyze Conditional Statements Using ConditionalGeometry 2 2 Analyze Conditional Statements Using Conditional
Conditional Statements Chapter 2 3 Analyze statements inConditional Statements Chapter 2 3 Analyze statements in
2 3 Conditional Statements Objectives v Analyze statements2 3 Conditional Statements Objectives v Analyze statements