CHAPTER 2
LESSON 2­3
OBJECTIVES
CONDITIONAL STATEMENTS
statements written in if­then form.
HYPOTHESIS
the "if" part of a conditional statement.
CONCLUSION
the "then" part of a conditional statement.
CONVERSE
exchanging the hypothesis and conclusion of the conditional statement.
INVERSE
negating both the hypothesis and conclusion of the conditional statement.
CONTRAPOSITIVE
negating both the hypothesis and conclusion of the converse statement.
LOGICALLY EQUIVALENT⇒ statements with the same truth values
CONDITIONAL: If p, then q.
CONVERSE: If q, then p.
INVERSE: If ~p, then ~q.
CONTRAPOSITIVE: If ~q, then ~p.
LOGICALLY EQUIVALENT⇒ statements with the same truth values
CONDITIONAL
CONTRAPOSITIVE
CONVERSE INVERSE
EXAMPLE
HYPOTHESIS, CONCLUSION
1) If two angles have a sum of 180, then they are supplementary.
2) The students will make an A, if they study.
Write in "if­then" form:
1) Sixteen years old can get a license.
If a person is sixteen years old, then he can get a license.
2) A square has 4 right angles.
If a polygon is a square, then it has 4 right angles.
Write the converse, inverse, and contrapositive for the given conditional statement. Decide the truth values.
1) If Bob lives in Prattville, then he lives in Alabama.
TRUE
CONVERSE: If Bob lives in Alabama, then he lives in Prattville. FALSE
INVERSE: If Bob does not live in Prattville, then he does not live in
Alabama. FALSE
CONTRAPOSITIVE: If Bob does not live in Alabama, then he does
not live in Prattville. TRUE
LESSON 2­3
CONDITIONAL STATEMENTS
Identify the hypothesis and conclusion of each statement.
1) If it is Saturday, then there is no school.
HYPOTHESIS:
CONCLUSION:
2) If x ­ 8 = 32, then x = 40.
HYPOTHESIS:
CONCLUSION:
3) If a polygon has four right angles, then the polygon is a rectangle.
HYPOTHESIS:
CONCLUSION:
Write each statement in if­then form.
4) All apes love bananas.
5) The sum of the measures of complementary angles is 90.
6) Collinear points lie on the same line.
Determine the truth value of each conditional statement. If false, give a counterexample.
7) If today is Wednesday, then yesterday was Friday.
8) If a is positive, then 10a is greater than a.
Determine the truth value of the following statement for each set of conditions.
If it does not rain this Saturday, we will have a picnic.
9) It rains this Saturday, and we have a picnic.
10) It rains this Saturday, and we don't have a picnic.
11) It doesn't rain this Saturday, and we have a picnic.
12) It doesn't rain this Saturday, and we don't have a picnic.
Write the converse, inverse, and contrapositive of each conditional statement. Identify which statements are true and which statements are false.
13) If you live in San Diego, then you live in California.
CONVERSE:
INVERSE:
CONTRAPOSITIVE:
14) If a polygon is a rectangle, then it is a square.
CONVERSE:
INVERSE:
CONTRAPOSITIVE:
15) If two angles are complementary, then the sum of their measures is 90.
CONVERSE:
INVERSE:
CONTRAPOSITIVE:
HOMEWORK on LESSON 2­3 p78­p79 16­44 even
HOMEWORK on LESSON 2­3 p78­p79 16­44 even
Attachments
Inductive Reasoning.notebook
2.3 Apply Deductive Reasoning.notebook