2-2 Conditional Statements

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Presentation transcript:

2-2 Conditional Statements

Conditional: is an if-then statement Hypothesis: is the part p following the if Conclusion: is the part of the q following then

Problem 1: Identifying the Hypothesis and the Conclusion What are the hypothesis and the conclusion of the conditional? If an animal is a robin, then the animal is a bird

Problem 1: Identifying the Hypothesis and the Conclusion What are the hypothesis and the conclusion of the conditional? If an angle measures 130, then the angle is obtuse.

Problem 2: Writing a Conditional How can you write the following statement as a conditional? Vertical angles share a vertex.

Problem 2: Writing a Conditional How can you write the following statement as a conditional? Dolphins are mammals.

Truth Value: of a conditional is either true or false To show it is true, show that every time the hypothesis is true the conclusion is also true (A counterexample can help you determine whether a conditional with a true hypothesis is true) To show it is false, find one counterexample for which the hypothesis is true and the conclusion is false, then the truth value of the conditional is false

Problem 3: Finding the Truth Value of a Conditional Is the conditional true or false? If false, find a counterexample. If a woman is Hungarian, then she is European.

Problem 3: Finding the Truth Value of a Conditional Is the conditional true or false? If false, find a counterexample. If a number is divisible by 3, then it is odd.

Negation: of a statement p is the opposite of the statement Negation: of a statement p is the opposite of the statement. ~𝑝 is read “not 𝑝” Statement: The sky is blue The negation would be: The sky is not blue.

Equivalent Statements: have the same truth value Conditional and Contrapositive (both are either true or false) Converse and Inverse

Problem 4: Writing and Finding Truth Values of Statements What are the converse, inverse, and contrapositive? What are the truth values of each? If a statement is false give a counterexample. If the figure is a square, then the figure is a quadrilateral

TRUE or FALSE (counterexample) Conditional: If the figure is a square, then the figure is a quadrilateral p: q: STATEMENT HOW IT IS WRITTEN TRUE or FALSE (counterexample) Converse Inverse Contrapositive

TRUE or FALSE (counterexample) Conditional: If a vegetable is a carrot, then it contains beta carotene p: q: STATEMENT HOW IT IS WRITTEN TRUE or FALSE (counterexample) Converse Inverse Contrapositive