2-2 Conditional Statements

Slides:

Advertisements

Similar presentations

Conditional Statements. Def: A Conditional is an if-then statement In symbols The hypothesis is the p-part And the conclusion is the q-part.

Advertisements

Conditional Statements

2.1 Conditional Statements

Section 2.1 Notes Conditional Statements. Conditional Statement A type of logic statement that has two parts: a hypothesis and a conclusion We will write.

2.2 Conditional Statements Goal: Students will be able:  To recognize conditional statements and their parts.  To write converses, inverses, and contrapositives.

2-2 Conditional Statements

Conditional Statements

2.1 Conditional Statements Goals Recognize a conditional statement Write postulates about points, lines and planes.

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,

2.1 Conditional Statements. Conditional Statement  Conditional statement has two parts, hypothesis and a conclusion.  If _____________, then____________.

Conditional Statements Conditional Statement: “If, then” format. Converse: “Flipping the Logic” –Still “if, then” format, but we switch the hypothesis.

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

2.2 Conditional Statements You can describe some mathematical relationships using a variety of if-then statements. A conditional – an if-then statement.

Logic and Proofs. 2-2 Conditional Statements Conditional statements are just that – statements that contain a condition. If p then q p is the Hypothesis.

Conditional Statements. Standards/Objectives: Students will learn and apply geometric concepts. Objectives: –Recognize and analyze a conditional statement.

Geometry - Section 2.1: Conditional Statements Conditional Statements Section 2.1 A logical statement with two parts: a hypothesis and a conclusion. Ex.

 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.

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

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

Conditional Statements Section 2-3 Conditional Statements If-then statements are called conditional statements. The portion of the sentence following.

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

Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form.

2-3 Conditional Statements- Related What are the three related conditional statements? How are the three related conditional statements made?

2.1 Conditional Statements Goal 1: Recognizing Conditional Statements Goal 2: Using Point, Line, and Plane Postulates CAS 1,3.

2.1 – Conditional Statements  Conditional Statement  If-Then Form  Hypothesis  Conclusion  Converse  Negation  Inverse  Contrapositive  Equivalent.

Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.

Section 2.1 Geometric Statements. Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is a logical statement that has two parts:

2-2 Conditional Statements Objectives: To recognize conditional statements and their parts To write converses, inverses, and contrapositives of conditionals.

2.1, 2.2 and 5.4: Statements and Reasoning. Conditional is an if-then statement that contains two parts. The part following the if is the Hypothesis.

CONDITIONAL STATEMENTS Intro to AlgebraFarris 2015.

Inductive and Deductive Reasoning. Notecard 30 Definition: Conjecture: an unproven statement that is based on observations or given information.

Inductive Reasoning Notes 2.1 through 2.4. Definitions Conjecture – An unproven statement based on your observations EXAMPLE: The sum of 2 numbers is.

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

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

Section 2.1 Conditional Statements Standards #1&3 Wednesday, July 06, 2016Wednesday, July 06, 2016Wednesday, July 06, 2016Wednesday, July 06, 2016.

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.

2.1 Conditional Statements

Conditional Statements

2-1 Vocabulary conditional statement hypothesis/conclusion

Conditional Statements

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

2-2 Conditional Statements

A logic statement written in if-then form.

2-2 Conditional Statements

2.1 Conditional Statements

Section 2.1 Conditional Statements

2.1 Conditional Statements

2.2 Analyze Conditional Statements

Conditional Statements

Conditional Statements

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

G7 Conditional Statements

2-2 Conditional Statements

More Conditional Statements

2.2 If - Then Statements OBJ: (1)To Write Statements in If-Then Form

2.4 Conditional Statements

Logic and Reasoning.

2-3 Conditional Statements

Section 1.7 and 1.8- Deductive Structure / Statements of Logic

Chapter 2 Reasoning and Proof.

Conditional Statements

2-2: Conditional Statements

Presentation transcript:

2-2 Conditional Statements

Examples If it is lightning, then practice will be cancelled If it is 3:20, then school is over. If you have a daughter, then you are a parent If 2 lines intersect, then they do so at one point If 2 planes intersect, then they do so at a line.

If p, then q. Hypothesis Conclusion These statements are called IF-THEN statements, or more formally known as CONDITIONALS. If p, then q. Hypothesis Conclusion

The words after IF and before THEN are part of the hypothesis. The words after THEN are part of the conclusion YOU DO NOT INCLUDE IF or THEN in either the hypothesis or the conclusion.

The TRUTH VALUE of a conditional is either true or false. In order to show a conditional is true, show that every time the hypothesis is true, the conclusion is also true. To show that conditional is false, you must find at least one counterexample for which the hypothesis is true and the conclusion is false.

The NEGATION of a statement p is the opposite of the statement The NEGATION of a statement p is the opposite of the statement. The symbol is ~p and is read “not p”. If you say the water is cold, the negation would be “the water is not cold” You use negations to write statements that are related to conditionals. Each conditional has 3 other statements that are closely related to the original conditional statement.

If you live in Ohio, then you live in Lima. Is this always true? What is one counterexample? Can you write the converse, inverse, and contrapositive? Identify the truth values of each.

Converses and counterexamples If you live in Lima, OH, then you live north of the Ohio River. Can you write the converse, inverse, and contrapositive? Identify the truth values of each.

If an angle is acute, then its measurement is less than 180. ORIGINAL Conditional If an angle is acute, then its measurement is less than 180. Converse Inverse Contrapositive

If two angles are adjacent, then they share a vertex. ORIGINAL Conditional If two angles are adjacent, then they share a vertex. Converse Inverse Contrapositive

When you find two statements that have the same truth value, then the statements are equivalent statements. Many texts refer to these statements being LOGICALLY EQUIVALENT (LE). Conditionals and contrapostives are always LE. Converses and Inverses are always LE.

HWK Section 2.2 in MathXLforSchool