Conditional Statements

1
Conditional Statements

• Section 2-1

2
Objectives

• To recognize conditional statements.
• To write converses of conditional statements.

3

• Have you ever heard a person say If you are
  not completely satisfied, then your money will be
  refunded?
• This is an if-then statement called a
  ______________.
• In symbols, we can write this as ________.
• This means, If p then q.

4

• Every conditional statement has two parts.
• The part following the if is the _____________.
• The part following the then is the ___________.

5
Example 1 Identify the Hypothesis and the
Conclusion

• If today is the first day of fall, then the
  month is September.
• Hypothesis
• Conclusion

6
Example 2 Identify the Hypothesis and the
Conclusion

• If you want to be fit, then get plenty of
  exercise.
• Hypothesis
• Conclusion

7
Example 3 Identify the Hypothesis and the
Conclusion

• If you can see the magic in a fairy tale, you
  can face the future.
• Hypothesis
• Conclusion

8
Example 4 Write each as a conditional

• a. A rectangle has four right angles.
• b. A tiger is an animal.
• c. An integer that ends with 0 is divisible by 5.

9

• The ______________ of a statement interchanges
  the hypothesis and conclusion.
• In symbols, we can write this as ________.
• This means, if q then p.

10
Write the converse of the conditional statement.

• Example 5
• If two lines are not parallel and do not
  intersect, then they are skew lines.

11
Write the converse of the conditional statement

• Example 6
• If you eat your vegetables, then you grow.

12
Write the converse of the conditional statement

• Example 7
• If a triangle is a right triangle, then it has a
  90 degree angle.

13
Truth Values (true or false?)

• Example 8 Write the converse of the
  conditional AND determine its truth value.
• If a figure is a square, then it has four sides.

14
Truth Values (true or false?)

• Example 9 Write the converse of the
  conditional AND determine its truth
  value.
• If two lines do not intersect, then they are
  parallel.

15
Truth Values (true or false?)

• Example 10 Write the converse of the
  conditional AND determine its truth value.
• If x 2, then x 2.

16
Truth Values (true or false?)

• Example 11 Write the converse of the
  conditional AND determine its truth value.
• If you travel from the United States to Kenya,
  then you have a passport.

17

• Use the following conditional for Exercises 13.
• If a circles radius is 2 m, then its diameter is
  4 m.
• 1. Identify the hypothesis and conclusion.
• 2. Write the converse.
• 3. Determine the truth value of the conditional
  and its converse.
• Show that each conditional is false by finding a
  counterexample.
• 4. If lines do not intersect, then they are
  parallel.
• 5. All numbers containing the digit 0 are
  divisible by 10.