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Math Help - Someone please explain how to solve a truth function in layman's terms.

  1. #1
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    Someone please explain how to solve a truth function in layman's terms.

    So I'm sitting in my logic grad course and the professor gives us this warm-up:

    Determine whether the given argument is valid or invalid.

    Premises: If I wash my car, then it will rain. It rained on Tuesday.
    Conclusion: I washed my car on Tuesday.

    He then proceeded to ask us what the answer was. A few hands went up. He called on the overachieving soccer mom-type in the front row and she says it is valid. Professor then asks how many people agree. A few hands went up. He then says, "complete the Venn diagram for this problem for the next class meeting." The WHOLE time, I'm thinking, "What is everyone talking about??" And the book has been no help, bc it assumes I know what all the symbols stand for. I've never taken a math class anywhere near this level.

    Can anyone please explain how to solve this problem??
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  2. #2
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    Re: Someone please explain how to solve a truth function in layman's terms.

    No, you can see from a counterexample that it isn't valid.

    If you wash your car on Thursday, and it rains on both Tuesday and Thursday, then the premise is true but the conclusion is false.

    I don't know about the venn diagram stuff, I'm not that into rigor :P Sorry, hopefully the above helps a bit though..
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  3. #3
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    Re: Someone please explain how to solve a truth function in layman's terms.

    here is what the venn diagram will look like:

    draw a circle, label it: days i washed my car (or maybe W for short).

    draw a larger circle around the first circle, label it: days it rains (or possibly R, to save on space). this captures the premise:

    if i wash my car, it will rain (the days you wash you car are a subset of all days that it rains).

    note that the R circle is BIGGER: it might rain on some days, but you didn't wash you car that day (for example, you might wash your car on Monday, but it rains all week, so Tuesday, Wednesday, Thursday, etc., it rained even though you didn't wash your car).

    finally, draw a circle inside R, but not totally inside W, like so (labelled T, for "Tuesday", or "this Tuesday"):

    Someone please explain how to solve a truth function in layman's terms.-circles.jpg

    this indicates that although you MAY have washed your car on Tuesday, and although Tuesday WAS a rainy day, you might not have washed your car on Tuesday, but some other day it rained.
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  4. #4
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    Re: Someone please explain how to solve a truth function in layman's terms.

    Hello, gfp45!

    So I'm sitting in my logic grad course and the professor gives us this warm-up:

    Determine whether the given argument is valid or invalid.
    Premises: .If I wash my car, then it will rain. .It rained on Tuesday.
    Conclusion: .I washed my car on Tuesday.

    He then proceeded to ask us what the answer was. .A few hands went up.
    He called on the overachieving soccer mom-type in the front row and she says it is valid.
    Professor then asks how many people agree. .A few hands went up.
    He then says, "complete the Venn diagram for this problem for the next class meeting."

    The WHOLE time, I'm thinking, "What is everyone talking about??"
    And the book has been no help, bc it assumes I know what all the symbols stand for.
    I've never taken a math class anywhere near this level.

    Sorry, I must make some observations . . . you won't like it.

    In your last paragraph, you sound like a Freshman (high school), not a grad student.
    . . "I don't know what's going on!"
    . . "The book sucks! .It doesn't explain anything!"
    . . "The teacher sucks! .He doesn't explain anything!"
    . . "The other students suck! .They're all geniuses!"
    . . "The course is WAY over my head!"

    Advice: .Drop the course and demand a refund.


    How far into the course are you?
    You make it sound like it's the first day of class
    . . and he's starting at Chapter Six.

    Since he mentioned Venn Diagrams,
    . . I assume you have been exposed to them.


    Just THINK about what is given to us (premises).
    . . "If I wash my car, then it will rain."

    Suppose someone else (Sam) made a claim (whether it's true or not):
    . . "Every time I wash my car, it rains."

    Then on a particular day, it rained.
    Can you conclude that Sam washed his car? .No!

    He did NOT say, "Every time it rains, I wash my car."


    Look at what can happen:

    . . . . . \text{I wash my car}\quad\to\quad \text{it rains}

    . . \text{I don't wash my car} \;\to\; \begin{Bmatrix}\text{it rains} \\ \text{or} \\ \text{it doesn't rain}\end{Bmatrix}

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  5. #5
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    Re: Someone please explain how to solve a truth function in layman's terms.

    Soroban! First of all, thank you for the PM, it was definitely a "duh!" moment for me. :-) Second, I don't mind at all that you get this impression from me because it is exactly how I felt on the first day of class when the professor began at chapter 3 (without prior notice). Lastly, because dropping the course is not an option I greatly appreciate all the help "geniuses", such as yourself, throw down at me. THANKS!!! :-)
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