Sec 2-2

1. 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.

2. 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

3. 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?

4. 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

5. 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.

7. 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 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.

8. 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 34-40 knots Beaufort Wind Scale for Open Sea 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 34-40 knots. Counterexample: Winds of 41-47 are strong gale

9. 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

10. P Q S R Conditional: If SR is Perpendicular to QR, then <SRQ measures 90° Converse: If <SRQ measures 90°, then SR is Perpendicular to QR. 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° Write the conditional and converse and determine if they are both true.

11. Today’s Work In Class: HW:.