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**Sec 2-2 Concept: Analyzing Conditional Statements**

Objective: Given a conditional statement, identify the hypothesis and conclusion, then be able to write the converse, negation, inverse and contrapositive and biconditional as measured by s.g.

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**Example 1: rewrite the conditional statement in if-then form**

All sharks have a boneless skeleton If a fish is a shark, then it has a boneless skeleton Can You? Identify the Hypothesis and Conclusion of the conditional statement

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**Example 2: Rewrite the conditional statement in if-then form**

All cows eat grass If an animal is a cow, then it eats grass Can you? Write the converse, inverse and contrapositive?

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**Example 2 Continued: Now Write the converse, inverse and contrapositive**

All cows eat grass Conditional: If an animal is a cow, then it eats grass Converse: if an animal eats grass, then it is a cow. Inverse: If an animal is not a cow, then it does not eat grass Contrapositive: If an animal does not eat grass, then it is not a cow

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**If a dog is a Great Dane, then it is large.**

Example 3: write the converse, inverse and contrapositive. Tell whether each statement is true or false. If a dog is a Great Dane, then it is large.

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**Beaufort Wind Scale for Open Sea**

Example 4: Winds At Sea: Use the portion of the Beaufort wind scale table shown to determine whether the biconditional statement is true or false. If false, provide a counterexample. A. A storm is a hurricane if and only if the winds of the storm measure 64 knots or greater. Beaufort Wind Scale for Open Sea Number Knots Description 8 34-40 Gale winds 9 41-47 Strong Gale 10 48-55 Storm 11 56-63 Violent Storm 12 64+ Hurricane TRUE To be true both the conditional and converse must be true. Conditional: If a storm is a hurricane, then the winds of the storm measure 64 knots or greater. Converse: If the winds of the storm measure 64 knots or greater, then the storm is a hurricane.

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**Beaufort Wind Scale for Open Sea**

Example 4 cont.: Winds At Sea: Use the portion of the Beaufort wind scale table shown to determine whether the biconditional statement is true or false. If false, provide a counterexample. B. Winds at sea are classified as a strong gale if and only if the winds measure knots Beaufort Wind Scale for Open Sea Number Knots Description 8 34-40 Gale winds 9 41-47 Strong Gale 10 48-55 Storm 11 56-63 Violent Storm 12 64+ Hurricane To be true both the conditional and converse must be true. Conditional: If a winds at sea are a strong gale, then the winds measure knots. Counterexample: Winds of are strong gale

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**Note: The biconditional becomes a definition**

Example 5: Rewrite the true statement in if-then form and write the converse. If the converse is true, combine it with the if-then statement to form a true biconditional statement. If the converse is false provide a counter example. Adjacent angles share a common side If-then: If 2 angles are adjacent, then they share a common side. Converse: If 2 angles share a common side, then they are adjacent. Biconditional: 2 angles are adjacent if and only if they share a common side. Note: The biconditional becomes a definition

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**TRUE SR is perpendicular to QR if and only if <SRQ measures 90°**

Example 6: Determine whether the biconditional statement about the diagram is true or false. IF false provide a counter example. TRUE SR is perpendicular to QR if and only if <SRQ measures 90° P Q S R Write the conditional and converse and determine if they are both true. Conditional: If SR is Perpendicular to QR, then <SRQ measures 90° Converse: If <SRQ measures 90°, then SR is Perpendicular to QR.

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Today’s Work In Class: HW:.

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EXAMPLE 1 Rewrite a statement in if-then form

EXAMPLE 1 Rewrite a statement in if-then form

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