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April 17th, 2019, 03:22 AM  #1 
Member Joined: Apr 2011 Posts: 36 Thanks: 0  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. 
April 17th, 2019, 06:27 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 
You've managed to completely confuse me!!

April 17th, 2019, 07:48 AM  #3 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,301 Thanks: 960 Math Focus: Wibbly wobbly timeywimey stuff.  
April 17th, 2019, 08:41 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
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. 
April 17th, 2019, 10:38 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  

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implication, logic 
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