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Math Help - Modus Ponens or Modus Tollens

  1. #1
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    Modus Ponens or Modus Tollens

    I am confused by these. Here is the problem:

    For each of the following pairs of statements, use Modus Ponens or Modus Tollens to fill in the blank line so that a valid argument is presented.

    a) If Janice has trouble starting her car, then her daughter Angela will check Janice's spark plus.
    Janice had trouble starting her car.
    ∴ ___________________________________

    b) If Brady solved the first problem correctly, then the answer he obtained is 137.
    Brady's answer to the first problem is not 137.
    ∴ ___________________________________

    c) If this is a repeat-until loop, then the body of this loop is executed at least once.
    _____________________________________
    ∴ The body of the loop is executed at least once.

    d) If Tim plays basketball in the afternoon, then he will not watch television in the evening.
    _____________________________________
    ∴ Tim didn't play basketball in the afternoon.


    Here is what I have:
    a) Her daughter Angelawill check Janice's spark plugs
    b) Brady did not solve the problem correctly
    c) This is a repeat-until loop
    d) Tim watched television in the evening

    I'm just not sure how to write these using Modus Ponens or Modus Tollens. Confusing.
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  2. #2
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    Re: Modus Ponens or Modus Tollens

    Quote Originally Posted by rhymin View Post
    For each of the following pairs of statements, use Modus Ponens or Modus Tollens to fill in the blank line so that a valid argument is presented.

    a) If Janice has trouble starting her car, then her daughter Angela will check Janice's spark plus.
    Janice had trouble starting her car.
    ∴ ___________________________________

    b) If Brady solved the first problem correctly, then the answer he obtained is 137.
    Brady's answer to the first problem is not 137.
    ∴ ___________________________________

    c) If this is a repeat-until loop, then the body of this loop is executed at least once.
    _____________________________________
    ∴ The body of the loop is executed at least once.

    d) If Tim plays basketball in the afternoon, then he will not watch television in the evening.
    _____________________________________
    ∴ Tim didn't play basketball in the afternoon.


    Here is what I have:
    a) Her daughter Angelawill check Janice's spark plugs
    b) Brady did not solve the problem correctly
    c) This is a repeat-until loop
    d) Tim watched television in the evening

    I'm just not sure how to write these using Modus Ponens or Modus Tollens. Confusing.

    I am really confused too. Are you saying that you don't know which is which?
    You have the correct answers for the 'blanks'. So what is your question?
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  3. #3
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    Re: Modus Ponens or Modus Tollens

    Well the textbook said to use Modus Ponens or Modus Tollens to fill in the blank, which should look something like this:

    [p ^ (p → q)] → q

    or

    p → q
    q
    ______
    ∴p

    But, I'm not quite sure how exactly to write these out.
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  4. #4
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    Re: Modus Ponens or Modus Tollens

    Quote Originally Posted by rhymin View Post
    Well the textbook said to use Modus Ponens or Modus Tollens to fill in the blank, which should look something like this:

    [p ^ (p → q)] → q

    or

    p → q
    q
    ______
    ∴p

    But, I'm not quite sure how exactly to write these out.
    I really think that you are over-thinking this question.
    As far as I am concerned, I taught this for over forty years, you have completed the question correctly.
    You have correctly applied the rules.

    Now, I am not your instructor. So I cannot be sure what you mean,
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  5. #5
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    Re: Modus Ponens or Modus Tollens

    Okay thank you. I guess I was over thinking it. I just got confused because the examples go very in depth with the "p, q, ∴, →, , etc." symbols and letters and it is very hard for me to follow.
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