Notes on Logic Continued

Slides:

Advertisements

Similar presentations

Conditional Statements

Advertisements

Bell Work 1) Write the statement in “If/Then” Form. Then write the inverse, converse, and contrapositive: a) A linear pair of angles is supplementary.

Biconditional Statements and Definitions 2-4

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide Logic The Study of What’s True or False or Somewhere in Between.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide Logic The Study of What’s True or False or Somewhere in Between.

Analyzing Conditional Statements A _______________________________ is a logical statement that has two parts, a hypothesis and a conclusion.

Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That.

Logic Disjunction A disjunction is a compound statement formed by combining two simple sentences using the word “OR”. A disjunction is true when at.

Biconditionals & Definitions. Biconditional Statement Contains the phrase “if & only if” Abbr. iff It is a conditional statement & its converse all in.

2.2 Definition and Biconditional Statements Use definitions and biconditional statements.

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.

Holt Geometry 2-4 Biconditional Statements and Definitions 2-4 Biconditional Statements and Definitions Holt Geometry Warm Up Warm Up Lesson Presentation.

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

Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement.

Conditional Statements

Section 2-1 Using Deductive Reasoning. If/then statements Called conditional statements or simply conditionals. Have a hypothesis (p) and a conclusion.

 What are conditionals & biconditionals?  How do you write converses, inverses, and contrapositives?

Unit 2 Part 1 Conditional, Converse, Inverse, and Contra- Positive Statements.

Section 2.2 Conditional Statements 1 Goals Recognize and analyze a conditional statement Write postulates about points, lines, and planes using conditional.

Section 2-1 Conditional Statements. Conditional statements Have two parts: 1. Hypothesis (p) 2. Conclusion (q)

Section 2.2 Analyze Conditional Statements. Homework Pg 82 #3-5, 11-15,

Section 2-2: Conditional Statements. Conditional A statement that can be written in If-then form symbol: If p —>, then q.

Unit 01 – Lesson 07 – Conditional Statements

Holt Geometry 2-4 Biconditional Statements and Definitions 2-4 Biconditional Statements and Definitions Holt Geometry Warm Up Warm Up Lesson Presentation.

2.2 Analyze Conditional Statements

Recall Section 2-3: Biconditionals & Definitions Objectives:

2.2 Definitions and Biconditional Statements

Section 2-2: Biconditionals and Definitions. Conditional: If two angles have the same measure, then the angles are congruent. Converse: If two angles.

Chapter 2: Reasoning & Proof 2.2 Biconditionals & Definitions.

 If an integer ends with 0, then the integer is divisible by 2.  What is the truth value of the above conditional?  What is the converse?  What is.

Success Criteria:  I can write good definitions  I can identify good definitions Today 1.Do Now 2.Check HW #13 3.Lesson HW # 14 Do Now Write a.

What is a Biconditional Students will be able to: 1.Rewrite compound sentences in conditional form 2.Find the biconditional of a conditional 3.Tell when/why.

Unit 2-2: Conditional Statements Mr. Schaab’s Geometry Class Our Lady of Providence Jr.-Sr. High School

Conditional Statments. Warm Up What is the fourth point of plane XUR Name the intersection of planes QUV and QTX Are point U and S collinear?

Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

2-3 Biconditionals and Defintions. Biconditional- a statement that is the combination of a conditional statement and its converse. If the truth value.

Lesson 2-1 Conditional Statements 1 Lesson 2-3 Conditional Statements.

EXAMPLE 4 Write a biconditional Write the definition of perpendicular lines as a biconditional. SOLUTION Definition: If two lines intersect to form a right.

Section 2.2 Homework Quiz Question Put the following Conditional Statement into If Then Form: All birds have feathers.

Conditional & Biconditional Statements Chapter 2 Section 4.

2.2 Definitions and Biconditional Statements

Analyze Conditional Statements

Conditional Statements

2-1 Vocabulary conditional statement hypothesis/conclusion

2-1 Vocabulary conditional statement hypothesis/conclusion

Conditional Statements

Definitions and Biconditional Statements

EXAMPLE 4 Write a biconditional

Objective Students will… Write and analyze biconditional statements.

2.2 Analyze Conditional Statements

Conditional Statements

Biconditional Statements and Definitions 2-4

Biconditional Statements and Definitions 2-4

Biconditional Statements and Definitions 2-4

2.2 Definitions and Biconditional Statements

Biconditional Statements and Definitions 2-4

Biconditional Statements and Definitions 2-2

Biconditional Statements and Definitions 2-4

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Biconditional Statements and Definitions 2-4

Conditional Statements

Conditional Statements

Section 2.2 Definitions and Biconditional Statement

CHAPTER 3 Logic.

Biconditional Statements and Definitions 2-4

Conditional Statements

2.1 Continued: Definitions and Biconditionals

Conditional Statements

Different Forms of Conditional Statements

Presentation transcript:

Notes on Logic Continued Analyze Conditional Statements Lesson 4.3 Page 204

Warm – up What is the converse of the conditional statement? If 2 lines are perpendicular, then they intersect and form a right angle (definition of perpendicular lines). Converse: If two lines intersect and form a right angle, then they are perpendicular. Is the conditional statement true or false? Is the converse true or false?

Definition of Equivalent Statements When two statements are both true or both false, they are called equivalent statements. *For example, definitions always produce a true conditional statement and a true converse (see previous slide). So, the definition of perpendicular lines and its converse are an example of equivalent statements. *A conditional statement and its contrapositive always have the same truth value.

Definition of a Biconditional Statement A biconditional statement is the combination of a conditional statement and its converse into one statement. The two statements are combined with the words “if and only if.” The symbol for “if and only if” is “iff.” *This is the only time that we don’t begin the sentence with the word “if,” but use “if and only if” in the middle of the sentence. *Since the statements are equivalent, it does not matter which one comes first.

Example Refer to the definition of perpendicular lines and its converse. The biconditional statement would be: Two lines are perpendicular if and only if they intersect and form a right angle. *An equivalent statement would be: Two lines intersect and form a right angle iff they are perpendicular.

True Biconditional Statements Biconditional statements are true if and only if its conditional statement and its converse are both true. Example: x = 3 iff . If x = 3, then . True or false? If , then x = 3. True or false? *Because the converse is false, the biconditional statement is also false.

Can this statement be made into a TRUE biconditional statement? Example #1 If a number ends in zero, then it is divisible by 5. Converse: If a number is divisible by 5, then it ends in zero. ANSWER: The conditional statement is true, but the converse is false. So the answer is NO.

Example #2 If , then x = 2 or –2. Converse: If x = 2 or –2, then Example #2 If , then x = 2 or –2. Converse: If x = 2 or –2, then . ANSWER: Since both statements are true, this may be written as a true biconditional statement. Biconditional Statement: iff x = 2 or –2.

Homework Assignment Page 207 # 1 – 3 and 5 – 10 all