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A little problem about mathmatical logic

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data
    1. Is there any difference between the following 2 signs?
    <=> (for biconditional) and 三(the equivalence sign)
    2. When we say 'P is defined as Q), do we mean P三Q?


    Thanks

    J

    2. Relevant equations



    3. The attempt at a solution
    It seems that for 2 propositions, P & Q:
    (i) P三Q when 'P and Q have the same kinds and numbers of components' and 'their truth values are equivalent'
    (ii) P <=> Q is expressing the same thing as above.
     
    Last edited: Nov 19, 2009
  2. jcsd
  3. Nov 24, 2009 #2
    plz help...
     
  4. Nov 24, 2009 #3

    HallsofIvy

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    Yes, the "biconditional" and "equivalence" are the same thing. And if "A" is defined as being "B", then A and B are equivalent.
     
  5. Nov 24, 2009 #4

    Hurkyl

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    For practical purposes, yes, they are effectively the same. The situation is similar to the four symbols [itex]\rightarrow, \implies, \vdash, \models[/itex].

    Any difference between them is in the minor details -- so unless you're studying those, you can treat them as essentially the same.

    From your description, it sounds like:
    1. [itex]P \Leftrightarrow Q[/itex] is a proposition, formed by connecting the propositions P and Q with the binary symbol [itex]\Leftrightarrow[/itex]? Or maybe your source is using [itex]P \leftrightarrow Q[/itex] for that....
    2. [itex]P \equiv Q[/itex] is an assertion about the syntactic and semantic properties of the two propositions P and Q.
     
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