Warm-up: What is the next term in the sequence? 1)3, 5, 11, 21, 35, ___ 2)
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Warm-up: What is the next term in the sequence? 1) 3, 5, 11, 21, 35, ___ 2)
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Transcript of Warm-up: What is the next term in the sequence? 1)3, 5, 11, 21, 35, ___ 2)
Warm-up:What is the next term in the sequence?
1) 3, 5, 11, 21, 35, ___
2)
• Objective: Students will write the inverse, converse, and contrapositive of a conditional statement.
• HW: - pg 75 #1-37 eoo
Review Homework
• Answers to even problems Pg 898:2: 0.03125
4: 9.0
6: 42
8: X=0
Inductive Reasoning
• Inductive Reasoning: a type of reasoning in which the conclusion is based on several past observations
• Ex:– 2, 5, 8, 11, 14, ___, ___– We have had pop quizzes on Friday for the
past four weeks…• Using inductive reasoning you would conclude that
we would likely have a quiz every Friday.
Deductive Reasoning
• Deductive Reasoning: a type of reasoning in which the conclusion is based on accepted statements.
• We used deductive reasoning to come up with the formula for the Distance Formula.
• Pythagorean Theorem
Conditional Statement(“If-then” statements)
• If it’s raining, then the game is canceled.– If p, then q.
• Hypothesis = it’s raining (“the condition”)
• Conclusion = the game is canceled.
Notation
If it’s raining, then the game is canceled.
Hypothesis = p = it’s raining
Conclusion= q = the game canceled
~p = (“not p”) it is NOT raining.
~q = (“not q”) the game is NOT canceled.
= implies
The Converse of a Conditional Statement
• If it’s raining, then the game is canceled.– If p, then q.
• If the game is canceled, then it’s raining.– If q, then p.
• The hypothesis and the conclusion are interchanged.
The Inverse of a Conditional Statement
• If it’s raining, then the game is canceled.– If p, then q.
• If it’s NOT raining, then the game is NOT canceled.– If not p, then not q.
• The hypothesis and the conclusion are negated.
The Contrapositive of a Conditional Statement
• If it’s raining, then the game is canceled.– If p, then q.
• If the game is NOT canceled, then it’s NOT raining.– If not q, then not p.
• The hypothesis and the conclusion are interchanged and negated.
Summary
Original
Converse
Inverse
Contrapositive pq ~~ qp ~~ pqqp
Example
• If you mow the lawn, then I will give you $10.
• What is the hypothesis?
• What is the conclusion?
• Write the converse of this statement.
• Write the inverse of this statement.
• Write the contrapositive of this statement.
Example
• If two angles are a linear pair, then the two angles are supplementary. (T/F)
• What is the hypothesis?
• What is the conclusion?
Example: Converse
• If two angles are a linear pair, then the two angles are supplementary. (T/F)
• Converse:
• If the two angles are supplementary, then the two angles are a linear pair. (T/F)
120° 60°
60°
120°
Example: Inverse
• If two angles are a linear pair, then the two angles are supplementary. (T/F)
• Inverse:
• If two angles are not a linear pair, then the two angles are not supplementary. (T/F)
120° 60°
60°
120°
Example: Contrapositive
• If two angles are a linear pair, then the two angles are supplementary. (T/F)
• Contrapositive:
• If two angles are not supplementary, then the two angles are not a linear pair. (T/F)
120° 60°
60°
120°
