Download Let`s Use Logic Geometry Investigation – Part 1 Deductive

Let’s Use Logic
Geometry Investigation – Part 1
Deductive Reasoning
The facts:
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Fred, Sam, Tom and Joe went fishing.
They caught six fish altogether.
Each man used a different kind of bait:
o Worms
o Eggs
o Flatfish
o Dry Flies.
One man caught three fish, another caught two, one caught
one, and one didn’t catch anything.
The one who caught two fish wasn’t Sam nor the one who
used worms.
The one who used the flatfish didn’t catch as many as Fred.
Dry Flies were the best lure of the day, catching three fish.
Tom used eggs.
 Sam didn’t use flatfish.
What did each man use for bait and how many fish did he catch? Discuss how you arrived at your answers.
You have just used your powers of deductive reasoning.
Definition: If you use facts, definitions, accepted properties and the laws of logic to form a logical argument,
then you have used deductive reasoning.
Geometry Investigation – Part 2
Inductive Reasoning
What comes next? Explain your reasoning for each answer?
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You have just used your powers of inductive reasoning.
Definition: If you find a pattern for specific cases and make a conjecture for the general case, then you have
used inductive reasoning.
NAME: ________________________ DATE: ______________ PERIOD: ___
Logic Begin Inductive Reasoning (Section 2.1)
Examples: Look at the numbers and find a ____________.
A) 1, 5, 9, 13
B) –7, -21, -63
C) 1, 3, 9, 27
D) 1,
2 1
, ,0
3 3
If you have a hunch/suspicion, make a guess. This guess is called a
________________. A _____________________ is an unproven statement that is based on
observations.
In science, we call a conjecture a ____________________.
How do you verify a conjecture? __________________________
The process that involves looking for patterns and making conjectures is called
_____________________________________.
Why do we use it?
To prove a conjecture true, you need to prove it true in ________________.
To prove a conjecture false, you need a single _______________________.
A _____________________________ is an example that shows a
conjecture is false.
EXAMPLES: Show the conjecture is false by finding a counterexample.
A) All odd numbers are prime.
B) All prime numbers are odd.
C) The sum of two numbers is always greater than the larger number.
D) If the product of two numbers is positive, then the two numbers must both be positive.
E) The absolute value of a number is always positive.
NAME: ________________________ DATE: ______________ PERIOD: ___
Geometry Notes Section 2.2 Part 1
Analyze Conditional Statement
A conditional statement has two parts: a ___________________ & a ________________.
When a statement is in the if-then form it goes:
If ______________________ then __________________.
Example: Identify the hypothesis and conclusion of this statement.
If the weather is warm, then we should go swimming.
Hypothesis:
Conclusion:
Example: Rewrite these sentences into conditional statements in if-then form.
a) An acute angle measures less than 90 .
b) All birds have feathers.
c) Today is Monday if yesterday was Sunday.
d) Write your own Conditional (If-then) statement about a rule in this class.
Examples: Decide if the statements are true or false. If false, write a counterexample.
a) If you visited New York, then you visited the Statue of Liberty.
b) If an angle is obtuse, then it measures more than 90 but less than 180 .
c) If the bell rings, then it is time to switch classes.
YOU TRY: WRITE SYMBOLS ALONG WITH THE SENTENCES
CONDITIONAL:
INVERSE:
CONVERSE:
CONTRAPOSITIVE:
Biconditional Statements
A _________________________ statement is a statement that contains the phrase
_________________ ( ______).
Writing a biconditional statement is equivalent to writing a conditional statement and its
converse.
_____________________ if and only if _____________________.
A __________________ statement is true ______________ and _____________ if any only if
both conditional statement and its converse are __________.
Examples: Rewrite the biconditional statement as a conditional statements and its
converse.
1) An angle is a right angle if and only if its measures 90 degrees.
Conditional:
Converse:
2) A point on a segment is the midpoint of the segment if and only if it bisects the segment.
Conditional:
Converse:
3. Three points are collinear if and only if they lie on the same plane.
Conditional:
Converse: