Objective: Children will be able to state the law of syllogism and use it to prove the validity of an argument.
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:
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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.
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2. If Mary sings then she will be happy. If Mary is happy then she will dance. Mary sings therefore Mary dances.
Argument 1 is invalid. The proof appears as follows:
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.
