Calculus Fall 2010 Lesson 01
Lesson Plan #009
Class: Geometry Date: Thursday October 15th/Friday October 16th
Topic: Connectives in logic (Continued) Aim: How do we determine if a compound sentence is a tautology?
HW #009: Page 4 of the lesson plan Objectives: 1) Students will be able to determine if a compound statement is a tautology
Do Now:
Build the truth table for the compound sentence [pic]
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PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Question:
What do you notice about every entry in the last column?
In logic, a tautology is a compound sentence that is always true, no matter what the truth values assigned to the simple sentences within the compound sentence. Determine if the compound sentence [pic]is a tautology by completing the table at right.
Determine if the compound statement below is a tautology by completing the table below.
|[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |
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What do you notice about the truth values in columns 4 and 5?
When two statements always have the same truth values, we say that the statements are logically equivalent. If you use the biconditional between two statements and you get a tautology then those two statements are logically equivalent.
Complete the table at right and determine which two statements are logically equivalent.
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Assignment #1: Let [pic]represent “I eat the right foods.” Let [pic]represent “I get sick.”
Sentences: If I eat the right foods, then I don’t get sick.
I don’t get sick or I don’t eat the right foods.
Express each of the two compound sentences in symbolic form then determine if the two compound sentences are logically equivalent.
Complete the truth table below
|[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |
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What can we tell about the statements in columns 5 and 6?
In column 5 we have a conditional statement and in column 6 we have the contrapositive of the conditional statement? What can we say about a conditional statement and its contrapositive?
How do you form the contrapositive of a conditional statement?
Here are two other related conditionals given the conditional [pic]
Inverse: [pic]
Converse: [pic]
Assignment:
Construct truth tables for the inverse and then the converse and see if it is logically equivalent to the original conditional
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Regents Questions:
1)
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2)
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A) B) C) D)
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5)
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HW# 9: Name __________________________________________ Date _______________ Period __________
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