Download Notes - Conditional Statements and Logic.notebook

1 ­ Notes ­ Conditional Statements and Logic.notebook
August 10, 2016
Conditional Statements
and
Inductive vs. Deductive Reasoning
Cobb Honors Standards 2.1 Use conjecture, inductive & deductive reasoning, counter examples, and informal proofs to justify mathematical arguments.
Aug 9­3:17 PM
What am I learning today?
How to write conditional statements and evaluate using inductive and deductive reasoning
How will I show that I learned it?
Evaluate the validity of conditional statements and their converses, inverses, and contrapositives.
Aug 9­3:18 PM
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1 ­ Notes ­ Conditional Statements and Logic.notebook
August 10, 2016
What is a conditional statement?
An "if ­ then" statement where the "if" part is the hypothesis and the "then" part is the conclusion.
Notation: p = hypothesis
q = conclusion
Aug 9­3:24 PM
Identify the hypothesis and conclusion in the following conditional statement.
If it is raining this afternoon, then band practice will be held inside.
Hypothesis:
Conclusion:
Aug 9­3:26 PM
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1 ­ Notes ­ Conditional Statements and Logic.notebook
August 10, 2016
Rewrite the following statement as a conditional statement if "if ­ then" form. You may need to add or subtract words.
All triangles have 3 sides.
Conditional Statement (p ⇒ q):
Aug 9­3:26 PM
Converse: take the conditional statement
and SWITCH the hypothesis and conclusion.
(think of a con-artist who switches things)
Find the converse of your conditional statement
If a polygon has 3 sides, then it is a triangle.
Converse Statement (q ⇒ p): Aug 9­3:26 PM
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1 ­ Notes ­ Conditional Statements and Logic.notebook
August 10, 2016
Inverse: take the conditional statement and
NEGATE the hypothesis and conclusion.
(think opposite)
Find the inverse of your conditional statement
If a polygon has 3 sides, then it is a triangle.
Inverse Statement (~p ⇒ ~q): Aug 9­3:26 PM
Contrapositive: take the conditional
statement and SWITCH and NEGATE the
hypothesis and conclusion.
Find the contrapositive of your conditional statement
If a polygon has 3 sides, then it is a triangle.
Contrapositive Statement (~q ⇒ ~p): Aug 9­3:26 PM
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1 ­ Notes ­ Conditional Statements and Logic.notebook
August 10, 2016
A counterexample is one example that can prove an entire statement false.
Example: If a number is prime, then it is an odd number.
Counterexample: Aug 9­3:32 PM
1) For the following conditional statement, find the converse, inverse, and contrapositive. 2) Then, state if each statement is true or false. 3) If a statement is false, provide a counterexample.
"If an angle measures 100o, then it is an obtuse angle."
Converse:
Inverse:
Contrapositive:
Aug 9­3:45 PM
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1 ­ Notes ­ Conditional Statements and Logic.notebook
August 10, 2016
Inductive Reasoning
Inductive Reasoning ­ specific to general. Based on evidence, generalize a conclusion to encompass all similar cases.
Example: Physically reflect A(­3, 5) & B(2, ­3) across the x­axis and get A'(­3, ­5) & B(­2, 3). Conclude that reflecting across the x­axis changes the sign of y.
Aug 9­3:49 PM
Deductive Reasoning
Deductive Reasoning ­ general to specific. Based on evidence and using definitions, theorems, and postulates, conclusion on result of specific case.
Example: Definition of perpendicular lines as intersecting at right angles. Definition of right angles as measuring 90o. Given two lines that intersect to make a 90o angle, conclude that the lines are perpendicular to one another.
Aug 9­3:49 PM
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1 ­ Notes ­ Conditional Statements and Logic.notebook
August 10, 2016
Homework: In the Textbook
p. 25, #14, 15, 17, 18, 20­27, 37, 38, 40
p. 33, #13­29, 38, 40, 41
p. 39, #2­3, 9­10
Aug 10­8:12 AM
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