1. 2.2 Analyzing Conditional Statements

2. Conditional Statements: Conditional Statement (In “If-Then” form): “If it is a bird, then it has feathers.” Ex. Conditional Statement: “All birds have feathers.” Ex. Conditional Statement: “All birds have feathers.” “If-Then” Form : If A ( Hypothesis ), then B ( Conclusion ) Hypothesis (A) Conclusion (B) are statements that can be put in “In-Then” form

3. On your own… Rewrite the conditional statements in if-then form: “All vertebrates have a backbone” “All triangles have 3 sides” “When x=2, x =4 2

4. Negation A statement that is the opposite of the original

5. T/F Decide whether each statement is true or false. If it is false, give a counterexample. __ Conditional (If-then) __ Converse __ Inverse __ Contrapositive Related Conditionals “Guitar players are musicians.” If A, then B If B, then A If not A, then not B If not B, then not A T/F Decide whether each statement is true or false. If it is false, give a counterexample. Hypothesis (A)Conclusion (B) “Guitar players are musicians.” If someone is a guitar player, then they are a musician If someone is a musician, then they are a guitar player T If someone is not a guitar player, then they are not a musician F F If someone is not a musician, then they are not a guitar player T

6. Conditional Statement: “If two angles form a linear pair, then they are supplementary.” T/F Decide whether each statement is true or false. If it is false, give a counterexample. __ Conditional (If-then) __ Converse __ Inverse __ Contrapositive “If two angles form a linear pair, then they are supplementary.” T “If two angles are supplementary, then they form a linear pair.” Conditional Statement: “If two angles form a linear pair, then they are supplementary.” F “If two angles do not form a linear pair, then they are not supplementary.” F “If two angles are not supplementary, then they do not form a linear pair.” T Conditional Statement: “If two angles form a linear pair, then they are supplementary.”

7. Conditional Statement: “If a dog is a Great Dane, then it is large.” T/F Write the converse, the inverse, and the contrapositive of the conditional statement. Tell whether each statement is true or false. If it is false, give a counterexample. __ Conditional (If-then) __ Converse __ Inverse __ Contrapositive “If a dog is a large, then it is a great Dane.” T F F T TRY ON YOUR OWN “If a dog is a Great Dane, then it is large.” “If a dog is not a Great Dane, then it is not large.” “If a dog is not large, then it is not a Great Dane.”

8. T/F Decide whether each statement is true or false. If it is false, give a counterexample. __ Conditional (If-then) __ Converse __ Inverse __ Contrapositive “If a polygon is equilateral, then the polygon is regular.” F “If a polygon is regular, then the polygon is equilateral.“ T “If a polygon is not equilateral, then the polygon is not regular.”.” T “If a polygon is not regular, then the polygon is not equilateral.“ F Conditional Statement: “All equilateral polygons are regular” FALSE

9. Biconditional Statement - a statement that contain the phrase “if and only if” - Used when both the conditional statement and it’s converse are true Ex: Definition: If two lines intersect to form a right angle, then they are perpendicular Converse: If two lines are perpendicular, then they intersect to form a right angle Biconditional: Two lines are perpendicular if and only if they intersect to form a right angle

10. Biconditional Statement On your own… If Mary is in the theater class, then she will be in the fall play. If she is in the fall play, then she must be in the fall play.