1 2.1 Conditional Statements List the characteristics of conditional statements Write converses of conditional statements.

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Presentation transcript:

1 2.1 Conditional Statements List the characteristics of conditional statements Write converses of conditional statements

2 Definition: Conditional Statement that can be written in If-then form Example A: –If it is Saturday, then there are no classes. If hypothesis, then conclusion. Hypothesis (the part after If): it is Saturday Conclusion (the part after then): there are no classes

3 Conditional: Example B If two lines are parallel, then they never intersect Hypothesis: two lines are parallel Conclusion: they never intersect

4 Conditional Statements in Math The following are different ways of writing the same statement in math: If p, then q p implies q p only if q p  q

5 Writing a Conditional Statement Many sentences without the words if and then can be written as conditionals. To do so, identify the sentence’s hypothesis and conclusion by figuring out which part of the statement depends on the other. Get a free tote bag with a one-year gym membership. –If you enroll with the gym for one year, then you get a free tote bag.

6 Truth Value of Conditional Statement True or False A conditional statement is false only when the hypothesis is true and the conclusion is false. –Example: If an integer is odd, then it is divisible by 3. False. 5 is an odd integer but it is not divisible by 3. To show that a conditional statement is false, find one counterexample where the hypothesis is true and the conclusion is false.

7 Writing the Converse of a Conditional The converse of the conditional switches the hypothesis with the conclusion. Conditional: If the animal is a cat, it has four legs. (True) Converse: If the animal has four legs, it is a cat. (False, a dog would a counterexample)

8 Converse Example Conditional: If two lines do not intersect, then they are parallel. (False, skew lines do not intersect either) Converse: If two lines are parallel, they do not intersect. (True)

9 Conditionals from Venn Diagrams Write a conditional statement from the following Venn diagram. If an animal is a blue jay, then it is a bird. Would the converse be true or false?

10 Learning Check and Summary What type of statement can be written in If-Then form? The If part of a conditional is known as the ___?____ The Then part of a conditional is known as the ___?____ To prove that a conditional statement is false, you try to find a ____?_____ If you rewrite a statement with the hypothesis and conclusion switched, the modified statement is known as the ___?____