Objectives Identify, write, and analyze the truth value of conditional statements. Write the inverse, converse, and contrapositive of a conditional statement.

Slides:

Advertisements

Similar presentations

9/2/2008 Warm Up Complete the conjecture by looking for a pattern in the diagram below. The number of sides of a polygon that has n vertices is________________.

Advertisements

Determine if each statement is true or false.

Geometry 2.2 Big Idea: Analyze Conditional Statements

Warm Up Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90°. 2. All perfect-square real numbers are positive.

Conditional Statements

Conditional Statements

When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process.

2.1 Conditional Statements

Conditional Statements

Warm Up Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90°. 2. All perfect-square numbers are positive. 3.

Holt Geometry 2-1 Using Inductive Reasoning to Make Conjectures Welcome to our Unit on Logic. Over the next three days, you will be learning the basics.

Holt Geometry 2-2 Conditional Statements Warm Up : Photographers and Cannibals Three National Geographic photographers and three cannibals are traveling.

10/21/2015Geometry1 Section 2.1 Conditional Statements.

Holt McDougal Geometry 2-1 Using Inductive Reasoning to Make Conjectures 2-1 Using Inductive Reasoning to Make Conjectures Holt Geometry Warm Up Warm Up.

Geometry CH 4-1 Using Logical Reasoning Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 6/1/2016Geometry4.

Logic and Reasoning. Identify the hypothesis and conclusion of each conditional. Example 1: Identifying the Parts of a Conditional Statement A.If today.

Inductive/Dedu ctive Reasoning Using reasoning in math and science.

Conditional Statements Lesson 2-1. Conditional Statements have two parts: Hypothesis ( denoted by p) and Conclusion ( denoted by q)

Conditional Statements

Chapter Conditional statements. * Identify, write, and analyze the truth value of conditional statements. * Write the inverse, converse, and contrapositive.

Warm Up Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90°. 2. All perfect-square numbers are positive. 3.

By phrasing a conjecture as an if-then statement, you can quickly identify its hypothesis and conclusion.

Holt Geometry 2-2 Conditional Statements 2-2 Conditional Statements Holt Geometry.

Holt McDougal Geometry 2-2 Conditional Statements 2-2 Conditional Statements Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.

Reasoning, Conditionals, and Postulates Sections 2-1, 2-3, 2-5.

2.2 Conditional Statements Objective: Students will analyze statements in if-then form and write the converse, inverse, and contrapositive of if-then statements.

Lesson 2-2 Conditional Statements 1 Lesson 2-2 Counterexamples.

Entry Task Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90°. 2. All perfect-square numbers are positive.

CONDITIONAL STATEMENTS Intro to AlgebraFarris 2015.

Holt Geometry 2-2 Conditional Statements 2-2 Conditional Statements Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.

Conditional Statements. 1) To recognize conditional statements and their parts. 2) To write converses, inverses, and contrapositives of conditionals.

Conditional Statements

Conditional Statements

Objectives Students will…

Introduction to Deductive Proofs

2-1 Vocabulary conditional statement hypothesis/conclusion

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

2-1 Vocabulary conditional statement hypothesis/conclusion

Objectives Students will…

Conditional Statements

Objectives Identify, write, and analyze the truth value of conditional statements. Write the inverse, converse, and contrapositive of a conditional statement.

Pearson Unit 1 Topic 2: Reasoning and Proof 2-2: Conditional Statements Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Copyright © 2014 Pearson Education, Inc.

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Lesson 2 – 3 Conditional Statements

More Conditional Statements

Conditional Statements

2-3 Conditional Statements

Conditional Statements

Math Humor Teacher: Which month has 28 days? Student: All of them!!

Conditional Statements

Conditional Statements

Conditional Statements

2-2: Conditional Statements

Presentation transcript:

Objectives Identify, write, and analyze the truth value of conditional statements. Write the inverse, converse, and contrapositive of a conditional statement.

By phrasing a conjecture as an if-then statement, you can quickly identify its hypothesis and conclusion.

Example 1: Identifying the Parts of a Conditional Statement Identify the hypothesis and conclusion of each conditional. A. If today is Thanksgiving Day, then today is Thursday. Hypothesis: Conclusion: B. A number is a rational number if it is an integer. Hypothesis: Conclusion:

Example 1C Identify the hypothesis and conclusion of the statement. "A number is divisible by 3 if it is divisible by 6." Hypothesis: Conclusion:

Example 2A: Writing a Conditional Statement Write a conditional statement from the following. An obtuse triangle has exactly one obtuse angle.

Example 2B: Writing a Conditional Statement Write a conditional statement from the following.

______________– true (T) or false (F) in a conditional statement ______________– true (T) or false (F) in a conditional statement. It is false only when the hypothesis is true and the conclusion is false. To show that a conditional statement is false, you need to find only one counterexample where the hypothesis is true and the conclusion is false.

Example 3A: Analyzing the Truth Value of a Conditional Statement Determine if the conditional is true. If false, give a counterexample. If this month is August, then next month is September.

Example 3B: Analyzing the Truth Value of a Conditional Statement Determine if the conditional is true. If false, give a counterexample. If two angles are acute, then they are congruent.

Example 3C: Analyzing the Truth Value of a Conditional Statement Determine if the conditional is true. If false, give a counterexample. If an even number greater than 2 is prime, then 5 + 4 = 8.

If the hypothesis is false, the conditional statement is true, regardless of the truth value of the conclusion. Remember!

The ______________ of statement p is “not p,” written as ~p. The negation of a true statement is false, and the negation of a false statement is true.

Definition Symbols A ______________ is a statement that can be written in the form "If p, then q." The ______________ is the statement formed by exchanging the hypothesis and conclusion. The ______________ is the statement formed by negating the hypothesis and conclusion. The ______________ is the statement formed by both exchanging and negating the hypothesis and conclusion.

Example 4A: Biology Application Write the converse, inverse, and contrapositive of the conditional statement. Use the Science Fact to find the truth value of each. If an animal is an adult insect, then it has six legs.

Example 4A: Biology Application If an animal is an adult insect, then it has six legs. Converse: Inverse: Contrapositive:

Example 4B Write the converse, inverse, and contrapostive of the conditional statement “If an animal is a cat, then it has four paws.” Find the truth value of each. If an animal is a cat, then it has four paws.

Example 4B If an animal is a cat, then it has four paws. Converse: Inverse: Contrapositive:

_____________________- Related conditional statements that have the same truth value. ______________- A conditional and its contrapositive are logically equivalent, and so are the converse and inverse.