Propositional logic Discrete Mathematics

  1. [SOLVED] Propositional logic Discrete Mathematics

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

    Assuming atleast one of the following statements is true, which one is it? why?

    a. Exactly one of these statements is true
    b. Exactly two of these statements are true
    c. Exactly three of these statements are true
    d. Exactly four of these statements are true
    e. Exactly five of these statements are true


    2. Relevant equations
    These are propositions, which can either be true or false, but not both. Total number of statements = 5 hence n = 5. Atleast one is true so n-1

    3. The attempt at a solution
    Inputting the above equation n-1=4, so exactly four of these statements is true. d points to this statement, which is true.
     
  2. jcsd
  3. Can someone please verify whether I am right or not? Thanks a lot
     
  4. matt grime

    matt grime 9,395
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    Why did you introduce n?

    Anyway, I see absolutely no logic in your argument.

    Is it possible for two of those statements to be true?
     
  5. It is possible for more than one of these statements to be true. I have come up with n because of the number of statements is 5 and assigned n to the number of statements. If you feel this is not right, you could point me in the right direction and I could get started on that.
     
  6. matt grime

    matt grime 9,395
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    What does assigning n to be the number of statements do? Look, just read the statements and please think again about what I said. Is it possible for two of those statements to be simultaneously true? (This is a BIG hint, so please don't ignore it again.)
     
  7. Thank you for the hint. I will surely look into it.
     
  8. in general try to assume one of the solutions is correct and see if you reach a contradiction
     
  9. I made up a truth table (I know this is a crude way) but also came up with 4 Truth values. Now, if all the statements are true then the fifth statement which is the conclusion is true also, else it is false. So, a,b,c and d are true?
     
  10. Dick

    Dick 25,887
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    You ignored matt again. Two of the statements can't be true at the same time. They would contradict each other.
     
  11. matt grime

    matt grime 9,395
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    For the love of God will you just think for a second! Every pair of statements are contradictory! Look, you've got me using exclamation marks, that's how annoyed I am: imagine I'm smacking my head against the desk. That's what you've driven me to.

    You honestly don't see that two things like:

    a) exactly X of these statements are true
    b) exactly Y of these statements are true

    are mutually incompatible if X doesn't equal Y?
     
    Last edited: Sep 19, 2007
  12. Matt,

    Thanks. This is my first class at discrete math. I just got this assignment yesterday and am also attempting to solve this myself. Call me slow, but I guess everything comes to everyone at a different pace. You cant blame me for trying and I while I may be trying wrong, atleast I try. Eventually I will come up with the right answer.

    Thanks again for your help.
     
  13. matt grime

    matt grime 9,395
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    This has nothing to do with "discrete maths". Let me put it this way:

    I have 5 marbles.

    I tell you that exactly 4 of them are red. Then I tell you that exactly 3 of them are red. Can I have been telling you the truth both times? Of course not. I cannot tell you two contradictory statements about the same thing and have them both be true.
     
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