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Basic Discrete math question

  1. Jan 8, 2015 #1
    Before I make a fool of myself let me just say I just had my first class today and the book/ teacher aren't helpful in my question. And I'm not even sure I'm in the right section, this is just my major

    1. The problem statement, all variables and given/known data

    "If 1+1=3 then 2+2=4"

    2. Relevant equations
    We just covered conditional statement and its truth table that states if p is false and q is true, then the statement is still true

    3. The attempt at a solution

    Basic question, following the table given to us, but it doesn't makes sense to me. If 1+1=3 then 2+2=4 , how can the whole statement be true?
     
  2. jcsd
  3. Jan 8, 2015 #2

    Mark44

    Staff: Mentor

    Yes
    To quote what you wrote above,
     
  4. Jan 8, 2015 #3
    WHat I was trying to say is that, it doesn't make sense to me ( how i see it ) that if I state 1+1 = 3 then 2+2=4 then why would the whole statement be true if only half of it is in realitiy.
     
  5. Jan 8, 2015 #4

    Mark44

    Staff: Mentor

    To re-quote what you wrote above,
    p: 1 + 1 = 3 (false)
    q: 2 + 2 = 4 (true)
    ##p \Rightarrow q## (true)

    From the truth table for an implication, the only pair of values of p and q that make the implication false are when p is true and q is false. All other pairs of values for p and q yield a true implication.
     
    Last edited: Jan 8, 2015
  6. Jan 8, 2015 #5

    haruspex

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    I think the important point is being missed.
    Let S be the statement "if p then q". If it turns out that p is false then the statement S is true regardless of whether q is true.
    Thus "if 1+1=3 then 2+2=9" is also a true statement.
    To put it in everyday language, if you start from a false premise then you can deduce anything.
    It is possible that the questioner wants you to illustrate this by a chain of argument that starts with "1+1=3" as a given and ends with "2+2=4". Or, better, ends with "2+2=9".
    Here's how you could do the last one:
    1+1=3
    2+2 = 1+1+1+1 = (1+1)(1+1) = (1+1)2 = 32 = 9
     
  7. Jan 8, 2015 #6

    Mark44

    Staff: Mentor

    I could be wrong, but that's not my take on this problem, which is to recognize that p (1 + 1 = 3) is false, so no matter what q is, the overall implication is true.
     
  8. Jan 8, 2015 #7

    haruspex

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    Yes, I said it was just a possibility. Without seeing the original question verbatim it's hard to know.
    But the main point I wanted to make is that this
    is misleading by being insufficiently general. It should say
    if p is false then the statement is true regardless of the truth or falsehood of q​
     
  9. Jan 9, 2015 #8

    RUber

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    The truth of the statement is based on the truth or falsehood of the logic, not the parts. The logic is ##p \implies q##. If p is not true, then the logic is true by virtue of the fact it cannot be proven false. There is a large gap between true and useful logic. This logic is true but totally useless, since p is never true.
     
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