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2-2 Conditional Statements

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Presentation on theme: "2-2 Conditional Statements"— Presentation transcript:

1 2-2 Conditional Statements

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

3 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

4 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.

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

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

7 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

8 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.

9 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.

10 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.

11

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

13 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

14 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

15 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

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