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2-1: Conditional Statements

Learn about conditional statements in logic, including the structure of hypothesis and conclusion. Practice writing conditionals and finding counterexamples to test truth values.

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2-1: Conditional Statements

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  1. Chapter 2 2-1:Conditional Statements

  2. Conditional • Also referred to as an “if-then” statement: • “If you are not completely satisfied, then your money will be returned.” Every conditional has two parts, the hypothesis and the conclusion.

  3. Hypothesis • The part following “if”: • “If you are not completely satisfied, then your money will be returned.” • Hypothesis: You are not completely satisfied.

  4. Conclusion • The part following “then” • “If you are not completely satisfied, then your money will be returned.” • Conclusion: Your money will be returned.

  5. Identify the hypothesis and conclusion: If y – 3 = 5, then y = 8. Hypothesis: y – 3 = 5 Conclusion: y = 8 If today is the first day of fall, then the month is September. Hypothesis: Today is the first day of fall. Conclusion: The month is September.

  6. Writing a Conditional • Write each sentence as a conditional: (remember, if-then statements) A rectangle has four right angles. A tiger is an animal. If it is a rectangle, then it has four right angles. If it is a tiger, then it is an animal.

  7. Writing a Conditional • Write the sentence as a conditional: (remember, if-then statements) An integer that ends with 0 is divisible by 5. If an integer ends with 0, then it is divisible by 5.

  8. Finding a Counterexample • A conditional can have a truth value of true or false. To show that a conditional is true, show that every time the hypothesis is true, the conclusion is also true. • To show that a conditional is false, you need to find only one counterexample for which the hypothesis is true and the conclusion is false.

  9. Find a Counterexample • Show that the following conditionals are false by finding a counterexample: If it is February, then there are only 28 days in the month. If the name of a state contains the word North, then the state borders an ocean. February 2012 (Leap Year) North Dakota

  10. Homework • Section 2-1 • p. 83, #’s 1-18, 38-40, 54-58

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