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Definition of Compound Statement

  1. Jan 15, 2016 #1
    Hello,

    In my Real Analysis textbook (Schramm) they say that an example of compound statement would be "Either 1+1=2 or a pencil is a useful tool in neurosurgery." I was wondering why this isn't a non-statement since I don't see where the truth value of it would be. Thanks!
     
  2. jcsd
  3. Jan 15, 2016 #2

    WWGD

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    It is ultimately an "or" statement and its truth value depends on the truth value of both " Either 1+1=2" and " a pencil is a useful tool in neurosurgery" . If seen as a wff in sentence logic , it can be transcribed as " A or B" , then compound (using A,B) similar in Predicate Logic ( more precisely, FOL).
     
  4. Jan 16, 2016 #3

    Mark44

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    The idea here, with either ... or, is that exactly one of the two statements must be true for the compound statement to be true. In this case 1 + 1 = 2 is a true statement, but (presumably) "a pencil is a useful tool in neurosurgery" is false. Hence the compound statement is true.

    This problem may have come from an analysis book, but it really falls under General Math, so I moved this thread.
     
  5. Jan 16, 2016 #4

    symbolipoint

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    Two sentences combined with the conjunction OR
     
  6. Jan 16, 2016 #5

    HallsofIvy

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    You don't see the truth value? "1+ 1= 2" is true and "a pencil is a useful tool in neurosurgery" is false so the truth value of this statement I "true".
    ("A or B" is false only when A and B are both false. In all other cases its true.)
     
  7. Jan 16, 2016 #6

    Mark44

    Staff: Mentor

    That's what I said in post #3...
     
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