# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.04

## Logic and Set Theory

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## Sample Lesson Plan 1

Motivation: Place on board the following:

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Have class substitute a simple statement for each letter. For example p might be I go to school; q I learn; and r I succeed. Next substitute conditional statements for these simple statements. It now reads. If I go to school then I learn. If I learn then I succeed. Therefore (...) if I go to school then I succeed. Children may wish to read their results and should be encouraged to do so.

This is the law of syllogism and can be

written:

[(P > q) ^ (p> r) > (p>r)

Using the law of syllogism prove that the following arguments are valid or invalid:

Argument 1 is invalid. The proof appears as follows:

- 1. If John is smart then he will be the leader. If John is smart then he will make a speech. John is a leader therefore he will make a speech.
- 2. If Mary sings then she will be happy. If Mary is happy then she will dance. Mary sings therefore Mary dances.

p John is smart

q he will be the leader

r he will make a speech

(Invalid) p >q p>r

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You cannot deduce that if q then r since both are conclusions and one does not imply the other. There is no syllogism.

Argument 2 is Valid. The proof appears as follows:

p Mary sings

q she will be happy

r she will dance

(Valid)

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The law of syllogism is satisfied and therefore the argument is valid.