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2-2 Conditional Statements

Learn about conditional statements, hypotheses, conclusions, truth values, and how to identify, write, and analyze conditionals. Practice finding truth values with examples.

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2-2 Conditional Statements

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  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. is read “not ” Statement: The sky is blue The negation would be: The sky is not blue.

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

  12. 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

  13. Conditional: If the figure is a square, then the figure is a quadrilateral p: q:

  14. Conditional: If a vegetable is a carrot, then it contains beta carotene p: q:

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