2.3 Deductive Reasoning (Monty Python)
September 16, 2009
2­3 Deductive Reasoning
Logic and Monty Python's Quest for the Holy Grail
Objective:
Use the law of detachment and the law of syllogism.
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2.3 Deductive Reasoning (Monty Python)
weighs as much
as a duck
September 16, 2009
witches
Write a conditional to describe the above Venn diagram.
If she is a witch, then she weighs as much as a duck!
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2.3 Deductive Reasoning (Monty Python)
September 16, 2009
If I give you this conditional
If she is a witch, then she weighs as much as a duck!
AND tell you that someone is a witch, what is the only conclusion you can make?
They weigh as much as a duck!
This is called the Law of Detachment
If a conditional is true and it's hypothesis is true, the the conclusion is true.
Symbolic Form: If p q is a true statement and p is true, then q is true.
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2.3 Deductive Reasoning (Monty Python)
September 16, 2009
For the given true statements, what can you conclude?
1. If it is made of wood, then it floats on water.
My boat is made of wood.
Conclusion:
Using the Law of Detachment, your only conclusion is that my boat floats on water.
2. If M is the midpoint of a segment, then it divides the segment into two congruent segments.
M is the midpoint of AB.
Conclusion:
Using the Law of Detachment, your only conclusion is that AM = MB.
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2.3 Deductive Reasoning (Monty Python)
September 16, 2009
Here are two conditionals that we will assume true:
If she is a witch, then she weighs as much as a duck.
If she weighs as much as a duck, then she floats on water.
What conclusion can you make from the above statements?
If she is a witch, then she floats on water!
This is called the LAW OF SYLLOGISM
If p q and q r are true statements, then p r is a true statement.
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2.3 Deductive Reasoning (Monty Python)
September 16, 2009
For the given statements, what can you conclude?
1. If a number is prime, then it does not have repeated factors.
If a number does not have repeated factors, then it is not a perfect square.
Conclusion:
If a number is prime, then it is not a perfect square.
2. If a number is divisible by 10, then it is divisible by 5. If a number ends in 0, then it is divisible by 10. Conclusion:
If a number ends is 0, then it is divisible by 5.
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2.3 Deductive Reasoning (Monty Python)
September 16, 2009
HOMEWORK
p. 96 # 1­15, 27­31
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