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April 17th, 2019, 03:22 AM   #1
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implication

How can I convince students of the truth value of if P is false then P implies Q is true independent of what truth value Q takes? Is there any real life or a convincing argument for this? I have given the analogy of if being elected then you will abolish the death penalty which seems ok but rather crass. Are there any other examples?

Last edited by skipjack; April 17th, 2019 at 03:27 AM.
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April 17th, 2019, 06:27 AM   #2
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You've managed to completely confuse me!!
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April 17th, 2019, 07:48 AM   #3
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Math Focus: Wibbly wobbly timey-wimey stuff.
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Originally Posted by Denis View Post
You've managed to completely confuse me!!
And how is this a strange thing for you?

-Dan
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April 17th, 2019, 08:41 AM   #4
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OK so your proposal depends upon the nature of P.
It is not true for all possible statements P.

Your example introduces the conditional 'if'
another example might be

Whether in Rome or not, I eat pasta.

This implies I always eat pasta, but of course may be factually incorrect, depending upon Q.

A plain statement for P such as

My bike is broken, so I can't go to the fair does indeed depend upon the truth of P.


So you should gather a few examples like this and have you students work through possible types of statements for P and Q and predict the effects of the truth values of P, Q and P implies Q.
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April 17th, 2019, 10:38 AM   #5
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And how is this a strange thing for you?
-Dan
Touchay!!
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