2-1: Conditional Statements Chapter 2. Conditional Also referred to as an “if-then” statement: –“If you are not completely satisfied, then your money.

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Presentation transcript:

2-1: Conditional Statements Chapter 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.

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

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

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

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.

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.

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.

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

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