Conditional Statements Conditional - Conditionals are formed by joining two statements with the words if and then: If p, then q. The if-statement is the.

Slides:

Advertisements

Similar presentations

What is the length of AB What is length of CD

Advertisements

Conditional Statements Geometry Chapter 2, Section 1.

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

Inductive Reasoning and Conjecture “Proofs”

Lesson 2-3 Conditional Statements. Ohio Content Standards:

Conditional Statements youtube. com/watch SOL: G.1a SEC: 2.3.

2-2 Conditional Statements

Welcome to Interactive Chalkboard 2.3 Conditional Statements.

Conditional Statements

Chapter 2.3 Conditional Statements. Conditional Statement.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–2) Then/Now New Vocabulary Key Concept: Conditional Statement Example 1: Identify the Hypothesis.

conditional statement contrapositive

2.3 Analyze Conditional Statements. Objectives Analyze statements in if-then form. Analyze statements in if-then form. Write the converse, inverse, and.

Bellwork Find m  1 and m  2 if m  1 = 8x + 18 and m  2 = 16x – 6 and m  1 and m  2 are supplementary. A.m  1 = 106, m  2 = 74 B.m  1 = 74, m 

2-3 Conditional Statements You used logic and Venn diagrams to determine truth values of negations, conjunctions, and disjunctions. Analyze statements.

L OGIC. A conjecture is an educated guess that can be either true or false. A statement is a sentence that is either true or false but not both. Often.

Geometry 6.2 Inverses and Contrapositives. There are two other types of conditionals called the inverse and the contrapositive. Recall:Conditional StatementIF.

Lesson 2-3 Conditional Statements. 5-Minute Check on Lesson 2-2 Transparency 2-3 Use the following statements to write a compound statement for each conjunction.

Over Lesson 2–2 5-Minute Check 1 A.True; 12 + (–4) = 8, and a triangle has four sides. B.True; 12 + (–4)  8, and a triangle has four sides. C.False; 12.

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

Conditional Statements Learning Target: I can write converses, inverses, and contrapositives of conditionals.

2.1 Conditional Statements GOAL 1 Recognize and analyze a conditional statement. GOAL 2 Write postulates about points, lines, and planes using conditional.

Conditional Statements

CONDITIONALS. Conditional Statement: Any statement that is or can be written in if- then form. That is, If p then q.

Conditional Statements

Section 2-2: Biconditional and Definitions TPI 32C: Use inductive and deductive reasoning to make conjectures Objectives: Write the inverse and contrapositive.

2-3 C ONDITIONALS. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements.

MM1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive. BY: BETH MATHIS Terry Marshall Jr.

Chapter 2 Reasoning and Proof. 2.1 Inductive Reasoning and Conjecture Conjecture- an educated guess based on known information Inductive reasoning- reasoning.

1. Grab board/marker for your group 2. Do WarmUp below V S T M P R TP bisects VS and MR. VM is congruent to SR. MP = 9, VT = 6 Perimeter of MRSV = 62 Find.

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

MM1G2.b. Understand and use the relationships among the statement and it converse inverse and contrapositive. Destiny and Scott.

Conditional Statements Geometry Chapter 2, Section 1.

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

2.3 Conditional Statements 0 Conditional statement- a statement that can be written in if-then form.

Splash Screen Today in Geometry Lesson 2.1: Inductive Reasoning Lesson 2.2: Analyze conditional statements.

2-1 Conditional Statements GOALS 1. Recognize and analyze a conditional statement. 2. Write postulates about points, lines, and planes using conditional.

Conditional Statements A conditional statement is a statement that can be written in “if-then” form. The hypothesis of the statement is the phrase immediately.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–2) NGSSS Then/Now New Vocabulary Key Concept: Conditional Statement Example 1: Identify the.

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

1 Conditional Statements “IF-THEN”. If- Then Statements If- Then Statements are commonly used in everyday life. Advertisement might say: “If you buy our.

2.1 Inductive Reasoning and Conjecture 2.2 Logic 2.3 Conditional Statements 2.8 Angle Relationships Chapter 2: Reasoning & Proof.

Transparency 2 Review: Lesson 2-1 Mini-Quiz. Class Greeting.

Conditional Statements I CAN… Write conditional, converse, and biconditional statements.

Conditional Statements I CAN… Write conditional, converse, and biconditional statements.

Conditional Statements LESSON 2–3. Lesson Menu Five-Minute Check (over Lesson 2–2) TEKS Then/Now New Vocabulary Key Concept: Conditional Statement Example.

Lesson 3 Menu Warm-up Problems. Lesson 3 MI/Vocab conditional statement if-then statement hypothesis conclusion related conditionals converse Analyze.

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

Conditional Statements

Conditional Statements

2-3 Conditional Statements

Make a conjecture about the next item in the sequence. 1, 4, 9, 16, 25

Conditional Statements

Conditional Statements

Do Now! 1. Evaluate 5x2 – 3x for x = 2 Solve: 3(11x – 7) = 13x + 25.

SWBAT analyze statements in if-then form.

Chapter 2 Reasoning and Proof.

Welcome to Interactive Chalkboard

Just write down today’s question…

Logical Sequencing & Conditional Statements

Conditional Statements

Logic and Reasoning.

Conditional Statements

Presentation transcript:

Conditional Statements Conditional - Conditionals are formed by joining two statements with the words if and then: If p, then q. The if-statement is the hypothesis and the then- statement is the conclusion. Conditional statements are either true conditionals or false conditionals. A conditional is a false conditional when the hypothesis is true and the conclusion is false. A conditional can be shown to be false by using a counterexample.

Identify Hypothesis and Conclusion A. Identify the hypothesis and conclusion of the following statement. If a polygon has 6 sides, then it is a hexagon.

Identify Hypothesis and Conclusion A. Identify the hypothesis and conclusion of the following statement. Answer:Hypothesis: a polygon has 6 sides Conclusion: it is a hexagon If a polygon has 6 sides, then it is a hexagon. hypothesis conclusion

Identify Hypothesis and Conclusion B. Identify the hypothesis and conclusion of the following statement. Tamika will advance to the next level of play if she completes the maze in her computer game.

Identify Hypothesis and Conclusion B. Identify the hypothesis and conclusion of the following statement. Tamika will advance to the next level of play if she completes the maze in her computer game. Answer:Hypothesis: Tamika completes the maze in her computer game Conclusion: she will advance to the next level of play

Write a Conditional in If-Then Form B. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. A five-sided polygon is a pentagon.

Write a Conditional in If-Then Form B. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. A five-sided polygon is a pentagon. Answer:Hypothesis: a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon.

A. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Truth Values of Conditionals Yukon rests for 10 days, and he still has a hurt ankle.

A. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer:Since the result is not what was expected, the conditional statement is false. Truth Values of Conditionals The hypothesis is true, but the conclusion is false. Yukon rests for 10 days, and he still has a hurt ankle.

B. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Truth Values of Conditionals Yukon rests for 3 days, and he still has a hurt ankle.

B. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer:In this case, we cannot say that the statement is false. Thus, the statement is true. Truth Values of Conditionals The hypothesis is false, and the conclusion is false. The statement does not say what happens if Yukon only rests for 3 days. His ankle could possibly still heal. Yukon rests for 3 days, and he still has a hurt ankle.

C. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Truth Values of Conditionals Yukon rests for 10 days, and he does not have a hurt ankle anymore.

C. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer:Since what was stated is true, the conditional statement is true. Truth Values of Conditionals The hypothesis is true since Yukon rested for 10 days, and the conclusion is true because he does not have a hurt ankle. Yukon rests for 10 days, and he does not have a hurt ankle anymore.

D. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Truth Values of Conditionals Yukon rests for 7 days, and he does not have a hurt ankle anymore.

D. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer:In this case, we cannot say that the statement is false. Thus, the statement is true. Truth Values of Conditionals The hypothesis is false, and the conclusion is true. The statement does not say what happens if Yukon only rests for 7 days. Yukon rests for 7 days, and he does not have a hurt ankle anymore.

Conditionals, Converses, etc Conditional - If p, then q. Converse - If q, then p. Inverse – If not p, then not q. Contrapositive – If not q, then not p. Counterexample – If p, then not q. Rules of Logic: The truth value of a converse may or may not be the same as that of its conditional. The truth value of a conditional and its contrapositive are always the same. Likewise for a converse and an inverse.

Write the converse, inverse, and contrapositive of the statement All squares are rectangles. Determine whether each statement is true or false. If a statement is false, give a counterexample. Related Conditionals

Write the converse, inverse, and contrapositive of the statement All squares are rectangles. Determine whether each statement is true or false. If a statement is false, give a counterexample. Related Conditionals Conditional:If a shape is a square, then it is a rectangle. The conditional statement is true. First, write the conditional in if-then form. Write the converse by switching the hypothesis and conclusion of the conditional. Converse:If a shape is a rectangle, then it is a square. The converse is false. A rectangle with and w = 4 is not a square.

Inverse:If a shape is not a square, then it is not a rectangle. The inverse is false. A 4-sided polygon with side lengths 2, 2, 4, and 4 is not a square. The contrapositive is formed by negating the hypothesis and conclusion of the converse. Contrapositive:If a shape is not a rectangle, then it is not a square. The contrapositive is true. Related Conditionals