2.1 CONDITIONAL STATEMENTS10/2

Learning Targets

•I can find the truth value given a conditional and a converse

•I can rewrite a statement as a conditional and write the conditional’s converse.

If-Then Statements• Ex: If you spend more time studying for the exam, then you will get a better grade.

• Conditional – Another name for an if-then statement; has two parts…the part following if is the hypothesis, and the part following then is the conclusion

If-Then Statements• Ex: If you spend more time studying for the exam, then you will get a better grade.

• Hypothesis: • you spend more time studying for the exam.

• Conclusion: • you will get a better grade.

Identifying the Hypothesis and Conclustion

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

• If y – 3 = 5, then y = 8

• If two lines are parallel, then the lines are coplanar.

Writing a Conditional

•You are taking a sentence and rewriting it in if-then form.

Writing a Conditional

•An integer that ends with 0 is divisible by 5.

• If an integer ends with 0, then it is divisible by 5

Practice

1) An acute angle measures less than 90 degrees.

2) A square has four congruent sides.

3) Two skew lines do not line in the same plane.

Truth Value

•Every conditional has a truth value. •The truth value is either true or false.

• True - it has to be true all of the time. • False - you need to provide just one counterexample (an example that proves a statement false).

Finding Counterexamples

•If it is February , then there are only 28 days in the month.

•If x² ≥ 0, then x ≥ 0.

Converse •The converse of a conditional switches the hypothesis and conclusion.

•So… If THIS, then THAT becomes

If THAT, then THIS

Writing Converses

•EX :•Conditional: If two lines intersect to form right angles, then they are perpendicular.

•Converse: If two lines are perpendicular, then they intersect to form right angles.

You try…•Conditional : If x = 9, then x + 3 = 12

•Converse: __________________

Truth values with Converses

•If a conditional is true, it doesn’t necessarily mean the converse is true also. You need to be able to determine: 1) is a conditional true or false, and 2) is the converse true or false

• Example:

If a figure is a square, it has four sides.Step 1) Determine if the conditional is true or false.Yes, it is true.Step 2) write its converse.If a figure has four sides, then it is a square.Step 3) Determine the truth value. Remember, if it is false, you must provide a counterexample.False, a Rectangle

• Try:

Conditional: If x² = 25, then x = 5Truth Value of Conditional:Converse:Truth Value of Converse:

•Conditional: If x = 2, then = 2•Write the converse and find the truth values for both the conditional and converse.

• Symbolic Form

• Conditional pq (If p, then q)• Converse qp (if q, then p)

• 2-1 Packet• #1-13

Homework

•P. 71 #3-31 odd, 43, 45, 47