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. 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.

7. 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.

8. 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

9. 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

10. 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.

11. Today’s Work
In Class:
HW:.