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]

|[pic] |[pic] |[pic] |[pic] |[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.

|[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |

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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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|[pic] |[pic] |[pic] |[pic] |[pic] |

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Regents Questions:

1)

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2)

3)

A) B) C) D)

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HW# 9: Name __________________________________________ Date _______________ Period __________

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