Law Of Detachment/Law of Modus Tollens
Lesson Plan #010
Class: Geometry Date: Monday October 19th/Tuesday September 20th, 2020
Topic: The Law of Detachment Aim: How do we use the Law of Detachment?
HW #010: Objectives: 1) Students will be able to use the Law of Detachment
Do Now:
PROCEDURE:
Write the Aim and Do Now
|[pic] |[pic] |[pic] |[pic] |[pic] |
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Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Complete the above truth table.
When a compound statement is set up in this way, we are trying to establish a convincing argument. An argument consists of a series of statements called premises and a final statement called the conclusion.
The argument is valid if and only if, its premises are true and by using the laws or reasoning, these premises force the conclusion to be true.
Looking at the above argument again, we are given
[pic] and also
[pic] and it led to the conclusion
[pic][pic] We know this because the argument is a tautology, meaning that it is always true.
We have just proven a Law called the Law of Detachment or the Law of Modus Ponens
Assignment #1:
Use the Law of Detachment to state a correct conclusion from the given premises.
Assignment #2:
Assignment #3:
In one of our past lessons, we proved that if a given a conditional is true, then the contrapositive is true. This is called the Law of the Contrapositive.
[pic]
[pic][pic]
Assignment #4:
|Statements |Reasons |
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Assignment #5:
Assignment #6:
Complete the truth table below
|[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |
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What do we notice about the truth values in the last column?
Since the argument above formed is a tautology, we conclude the argument is valid.
The argument we have just tested is called the Law of Modus Tollens.
[pic]
[pic]
[pic][pic]
|Statements |Reasons |
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Assignment #7:
Given: [pic]
[pic]
Prove: [pic]
Assignment #8:
|Statements |Reasons |
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Given:
• You can take driver’s education if you are a senior
• You can’t take driver’s education this year
Prove:
• You are not a senior this year.
{Assign letters to represent individual statements, then us the letters in the proof}
HW#10 Name ________________________________________ Per. ___________ Date __________
[pic]
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Law of the contrapositive
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