Warm Up Write a conclusion to match the hypothesis:

Slides:

Advertisements

Similar presentations

SECTION 2.1 Conditional Statements. Learning Outcomes I will be able to write conditional statements in if- then form. I will be able to label parts of.

Advertisements

Conditional Statements

Conditional Statements

 Writing conditionals  Using definitions as conditional statements  Writing biconditionals  Making truth tables.

Notes on Logic Continued

2.2 Analyzing Conditional Statements. Conditional Statements: Conditional Statement (In “If-Then” form): “If it is a bird, then it has feathers.” Ex.

Conditional Statements

Analyze Conditional Statements

Conditional Statements

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

2.1 Conditional Statements

Lesson 2.2 Analyze Conditional Statements Goal: The learner will write definitions as conditional statements.

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

Wednesday, October 24 th Aim: In what other ways can we potentially change the truth value of a conditional statement? Do Now: Write a TRUE conditional.

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

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

Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the.

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.

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

Chapter 2.2 Notes: Analyze Conditional Statements Goal: You will write definitions as conditional statements.

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

Warm up 1.Re-write the following statements as an if-then statement. 2.State the converse of the statement. a.The midpoint of a segment is a point that.

 Outside across from the word: › write the symbol for conditional: p -> q  INSIDE: › How to write the statement : If p, then q. › Example : If an angle.

Lesson 2.2 Analyze Conditional Statements Goal: The learner will write definitions as conditional statements.

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

Inductive and Deductive Reasoning. Notecard 29 Definition: Conjecture: an unproven statement that is based on observations. You use inductive reasoning.

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.

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

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

2-2 Analyze Conditional Statements Hubarth Geometry.

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

Conditional Statements

Conditional Statements

Objectives Students will…

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

Classify each of the following angles as acute, right, or obtuse.

Analyze Conditional Statements

Lesson 2.2 Analyze Conditional Statements

Conditional Statements

Conditional Statements

What do you need more work on from the last unit?

Conditional Statements

Conditional Statements

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

Conditional Statements

Conditional Statements

2-2 Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Warmup State whether each sentence is true or false.

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Conditional Statements

Conditional Statements

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

Conditional Statements

Logic and Reasoning.

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

Conditional Statements

Conditional Statements

Presentation transcript:

Warm Up Write a conclusion to match the hypothesis: If I ride my bike down that steep hill, then _____________________ If an angle measures exactly 180 degrees, then ________________ Write a hypothesis to match the conclusion: _______________________________ then I am probably dreaming. _______________________________ then they are adjacent angles.

Conditional Statements Part 2

Review.. Conditional statement – logical statement that has two parts, a hypothesis (p), and a conclusion (q). Written in “if – then” form, the “if” part contains the hypothesis, and the “then” part contains the conclusion In words: If p, then q In math symbols: p q If Clark is a dog, then he has four legs hypothesis conclusion

Related Conditionals Negation – the opposite of the original statement In words: “not p” or “not q” In math symbols: ~p or ~q Example: The cat is black. (negation) The cat is NOT black Example: Chuck Norris is not awesome. (negation) Chuck Norris IS awesome. Converse – to write the converse of a conditional statement, just switch the hypothesis and conclusion In words: if q then p In math symbols: q p Example: If it is raining, then it is wet. (converse) If it is wet, then it is raining. Example: If x is even, then x is divisible by 2.(converse) If x is divisible by 2, then x is even.

Related Conditionals (cont’d.) Inverse – to write the inverse of a conditional statement, negate both the hypothesis and conclusion In words: If not p then not q In math symbols: ~p ~q Example: If I break my phone I will get grounded. (inverse) If I do not break my phone, I will not get grounded. Example: If you play guitar, then you are a musician. (inverse) If you do not play guitar, then you are not a musician.

Related Conditionals (cont’d.) Contrapositive – to write the contrapositive of a conditional statement, first write the converse. Then negate both the hypothesis and conclusion. In words: If not q then not p In math symbols: ~q ~p Example: If the year has 366 days then it is a leap year. (contrapositive) If it is not a leap year, then the year does not have 366 days. Example: If you throw a bucket of ice water on my head, then I will scream. (contrapositive) If I do not scream, then you will not throw a bucket of ice water on my head.

Related Conditionals (cont’d.) Biconditional statement – when a conditional statement and its converse are both true, you can write them as a single biconditional statement. It uses the phrase “if and only if.” These are often used in geometric definitions. In words: q if and only if q In math symbols: p q Example: If an angle is less than 90 degrees, then it is an acute angle. (biconditional) An angle is less than 90 degrees if and only if it is an acute angle. Example: If two lines intersect to form a right angle, then they are perpendicular lines. (biconditional) Two lines intersect to form a right angle if and only if they are perpendicular lines.