2.2 Conditional Statements and

2.3 Using deductive Reasoning to Verify Conjectures

Conditional (If-Then) Statement: A statement with two parts: an “if” part that contains the hypothesis and a “then” part that contains the conclusion

Hypothesis: The “if” part of an if-then statement (may be an implied “if”)

Conclusion: The “then” part of an if-then statement (may be an implied “then”)

Identify the hypothesis and the conclusion for each:

If a butterfly has a curved black line on its hind wing, then it is a Viceroy.A number is an integer if it is a natural number.The midpoint M of a segment bisects the segment.

Spiders

Tarantulas

Analyze the truth value of each statement:

If a butterfly has a curved black line on its hind wing, then it is a Viceroy.A number is an integer if it is a natural number.The midpoint M of a segment bisects the segment.

Spiders

Tarantulas

Conditional p → q

The inverse is the statement formed by negating the hypothesis and the conclusion (~p →~q)

The converse of a statement is formed by reversing the hypothesis and conclusion of the original conditional (q → p)

The contrapositive is the statement formed by both reversing the hypothesis and the conclusion AND negating the hypothesis and the conclusion. (~q → ~p)

Statement Example Truth Value

Conditional If m<A = 950, then <A is obtuse.

Converse

Inverse

Contrapositive

Practice Together

Textbook page 84 problems 1-12

Deductive Reasoning

Using logic to draw conclusions from given facts, definitions, and properties

Law of Detachment

If the hypothesis (p) of a TRUE if-then statement is true, then the conclusion (q) is also truep q, then true p true q If you are late to class, then you will be counted tardy.Mark is late to class.We conclude: Mark is counted tardy

Law of Syllogism

If p q and q r are true statements, then p r must be true as wellIf you do well on all of your homework, then you will do well on tests and quizzes. If you do well on tests and quizzes, then you will pass the class.If you do well on all of your homework, then you will pass the class

If the endpoints of a segment have the coordinates (-1, -2) an (5,2), then the midpoint is at (2,0).The endpoints of AB are at (-1, -2) an (5,2).

If the perimeter of a square is 20 ft, then the length of a side of a square is 5ft.If the length of a side of a square is 5 ft, then the area is 25 square ft.

Practice together

Textbook page 91 problems 1-8