Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Published byGordon Freeman Modified over 8 years ago

Similar presentations

Presentation on theme: "Lesson 2-2 Conditional Statements 1 Lesson 2-2 Counterexamples."— Presentation transcript:

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

2 A conditional statement has a truth value of either true (T) or false (F). 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.

3 Lesson 2-2 Conditional Statements 3 Conditional Statements can be true or false: A conditional statement is false only when the hypothesis is true, but the conclusion is false. A counterexample is an example used to show that a statement is not always true and therefore false. If you live in Texas, then you live in Corpus Christi. Statement: Counterexample:I live in Texas, BUT I live in Houston. Is there a counterexample? Therefore (  ) the statement is false. Yes !!!

4 Determine if the conditional is true. If false, give a counterexample. Example 3A: Analyzing the Truth Value of a Conditional Statement If this month is August, then next month is September. When the hypothesis is true, the conclusion is also true because September follows August. So the conditional is true.

5 Determine if the conditional is true. If false, give a counterexample. Example 3B: Analyzing the Truth Value of a Conditional Statement You can have acute angles with measures of 80° and 30°. In this case, the hypothesis is true, but the conclusion is false. If two angles are acute, then they are congruent. Since you can find a counterexample, the conditional is false.

6 Determine if the conditional is true. If false, give a counterexample. Example 3C: Analyzing the Truth Value of a Conditional Statement An even number greater than 2 will never be prime, so the hypothesis is false. 5 + 4 is not equal to 8, so the conclusion is false. However, the conditional is true because the hypothesis is false. If an even number greater than 2 is prime, then 5 + 4 = 8.

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

8 The negation 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.

Download ppt "Lesson 2-2 Conditional Statements 1 Lesson 2-2 Counterexamples."

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________________.

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________________.
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.

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.
Lesson 2-5 1 Conditional Statements. Lesson 2-5 2 Conditional Statement Definition:A conditional statement is a statement that can be written in if-then.

Lesson Conditional Statements. Lesson Conditional Statement Definition:A conditional statement is a statement that can be written in if-then.
Conditional Statements

Conditional Statements
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.

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

2.1 Conditional Statements
Do Now: 1.Copy Down HW. 2.Describe the pattern, then find the next two numbers in the pattern: 3, 12, 48, 192, …

Do Now: 1.Copy Down HW. 2.Describe the pattern, then find the next two numbers in the pattern: 3, 12, 48, 192, …
Conditional Statements and Logic 2.2 Ms. Verdino.

Conditional Statements and Logic 2.2 Ms. Verdino.
Conditional Statements

Conditional Statements
Conditional Statements

Conditional Statements
Find opposites of numbers EXAMPLE 4 a. If a = – 2.5, then – a = – ( – 2.5 ) = 2.5. b. If a =, then – a = –. 3 4 3 4.

Find opposites of numbers EXAMPLE 4 a. If a = – 2.5, then – a = – ( – 2.5 ) = 2.5. b. If a =, then – a = –
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.

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

Holt Geometry 2-2 Conditional Statements Warm Up : Photographers and Cannibals Three National Geographic photographers and three cannibals are traveling.
Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That.

Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That.
10/21/2015Geometry1 Section 2.1 Conditional Statements.

10/21/2015Geometry1 Section 2.1 Conditional Statements.
10/21/2015Geometry1 Conditional Statements. 10/21/2015Geometry2 Goals Recognize and analyze a conditional statement Write postulates about points, lines,

10/21/2015Geometry1 Conditional Statements. 10/21/2015Geometry2 Goals Recognize and analyze a conditional statement Write postulates about points, lines,
Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 6/1/2016Geometry4.

Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 6/1/2016Geometry4.
Warm Up Write a conditional statement from each of the following. 1. The intersection of two lines is a point. 2. An odd number is one more than a multiple.

Warm Up Write a conditional statement from each of the following. 1. The intersection of two lines is a point. 2. An odd number is one more than a multiple.
Inductive/Dedu ctive Reasoning Using reasoning in math and science.

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

Similar presentations

Ads by Google