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In a course I had, we have been given two statements P and Q and their "boolean table" : enter image description here

While I completely understand P and Q and P or Q values, I can't understand the first two lines for P->Q, why is the result true even when P is false ?

Thank you.

anomaly
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Pop Flamingo
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    This is a common question around these parts. http://math.stackexchange.com/search?q=if+p+then+q – turkeyhundt Sep 14 '16 at 18:50
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    Thank you ! Sorry, didn't knew how to formulate it in the search engine. – Pop Flamingo Sep 14 '16 at 18:54
  • Basically "if P then Q" does not imply any form of a causality. It's just the statement "whenever P is true, Q is true". It is equivalent to "it's not the case that P is true and Q is false". Basically if P is false "whenever P is true, Q is true" is vacuously true because we can't have the case that P is true and Q is false so when P is false $P \rightarrow Q$ is "not false".. – fleablood Sep 14 '16 at 19:34
  • @fleablood Oh thank you so much, yes, actually I was considering only P, not the whole statement (P->Q) ! – Pop Flamingo Sep 14 '16 at 19:40

1 Answers1

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Think of it this way. If $P$ is true, we test $P \rightarrow Q$ by seeing whether $Q$ is true or not.

In other words $P\rightarrow Q$ is falsified when $P$ is true but $Q$ is false. If $P$ is not true, we can't do any such falisifying verification.

So if $P$ is false, then $P \rightarrow Q$ is ... not false.

fleablood
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