Section 2.2 Homework Quiz Question Put the following Conditional Statement into If Then Form: All birds have feathers.

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Presentation transcript:

Section 2.2 Homework Quiz Question Put the following Conditional Statement into If Then Form: All birds have feathers.

Homework Question Answer If an animal is a bird then it has feathers.

Section 2.2 Conditional Statements

Vocabulary What is a Conjecture? An unproven statement based on observations. What is a Counterexample? A specific case for which a conjecture is wrong. What is a Conditional Statement? A logical statement with two parts, a hypothesis and a conclusion.

Conditional Statements If Then Form If is hypothesis Then is the conclusion Example: If you participate in class then you will get a better grade. Hypothesis: You participate in class Conclusion: You get a better grade

More Vocabulary Negation: Opposite of the original statement Example: The ball is red  The ball is not red Converse: Exchange the hypothesis and the conclusion in a conditional statement Example: If an animal has feathers then it is a bird.

Even More Vocabulary Inverse: Negate both the hypothesis and the conclusion. Example: If an animal is not a bird then it does not have feathers Contrapositive: Negate the hypothesis and conclusion of the converse Example: If an animal does not have feathers then it is not a bird.

What are Equivalent Statements Equivalent Statements: When two statements are both true or both false The Conditional Statement and Contrapositive – If an animal is a bird then it has feathers. – If an animal does not have feathers then it is not a bird. The Converse and Inverse – If an animal has feathers then it is a bird. – If an animal is not a bird then it does not have feathers

What is a Biconditional Statement? Biconditional Statement: A statement that contains the phrase “if and only if” When the conditional statement and its converse are both true – An animal is a bird if and only if it has feathers.

Perpendicular Lines If two lines intersect to form a right angle then they are perpendicular lines Converse If two lines are perpendicular lines then they intersect to form a right angle Biconditional Two lines are perpendicular if and only if they intersect to form a right angle