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Logical implication?

  1. Oct 2, 2004 #1
    Can someone try and explain it to me?
    I cannot understand the meaning of implication ( if p then q) from truth table

    p q p => q
    t t t
    t f f
    f t t
    f f t


    so it is if p is true then q is true or if p is false then q is false?

    then why if p is false and q is true, p implies q is true?
     
  2. jcsd
  3. Oct 2, 2004 #2

    mathman

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    Science Advisor
    Gold Member

    If p is false, q can be either true or false, therefore p=>q remains true. The only case where it is contradicted is p true and q false.
     
  4. Oct 3, 2004 #3

    matt grime

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    Science Advisor
    Homework Helper

    This is one I have to explain a lot to new students. Here's the example that I find useful.

    P is the statement 'n is divisible by 4'
    Q is the statement 'n is even'

    We can all agree that the proposition 'If P then Q ' is true, yep?

    But n=6 is a case where P is false and Q is true.
     
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