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keebler01

  • 3 years ago

Form the contrapositive: If I do not wash my clothes, then I will have nothing clean to wear. If I have nothing clean to wear, then I did not wash my clothes. If I do not wash my clothes, then I will have something clean to wear. If I wash my clothes, then I will have something clean to wear. If I have something clean to wear, then I washed my clothes. If I have something clean to wear, then I did not wash my clothes.

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  1. keebler01
    • 3 years ago
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    if i was wash my clothes, then i will have something clean to wear.

  2. polpak
    • 3 years ago
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    First identify your p and your q

  3. Alchemista
    • 3 years ago
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    I discussed this before. However, I will talk about it again.

  4. Alchemista
    • 3 years ago
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    The contrapositive of \(p \implies q\) is \(\neg q \implies \neg p\)

  5. Alchemista
    • 3 years ago
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    You can make sense of this intuitively, or by following the rules of modus ponens to prove it rigorously.

  6. Alchemista
    • 3 years ago
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    We will start by identifying the statements \[p = \text{ "I washed some clothes"} \]\[q = \text{ "I have something clean to wear"}\] We have \( \neg p \implies \neg q\) therefore the contrapositive is \(q \implies p\)

  7. polpak
    • 3 years ago
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    \[p: \text{I have nothing to wear}\]\[q:\text{I did not wash my clothes}\] You have an implication of the form: \[p\implies q\] The contrapositive is: \[\lnot q \implies \lnot p\] So first what is \(\lnot q\)? "I washed my clothes" What is \(\lnot p\) "I have something to wear" So the contrapositive of the original would be : If I washed my clothes, then I have something to wear

  8. polpak
    • 3 years ago
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    Or you can start with negated forms and swap them as Alchemista did.

  9. Alchemista
    • 3 years ago
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    Polpak your answer is wrong.

  10. Alchemista
    • 3 years ago
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    If I have something to wear, then I washed my clothes.

  11. polpak
    • 3 years ago
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    Oh, bother. I read the wrong statement as the original because of how it's formatted. "If I have nothing clean to wear, then I did not wash my clothes." I thought that was the original implication.

  12. Alchemista
    • 3 years ago
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    Might be a good idea to remove the answer, so as not to confuse the original poster.

  13. keebler01
    • 3 years ago
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    ok i think mine sounds right!

  14. polpak
    • 3 years ago
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    Well operating from the premise I gave, I'm correct. But my correct answer is not the answer to the original poster's question.

  15. Alchemista
    • 3 years ago
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    Keebler01, the correct answer is "If I have something clean to wear, then I washed my clothes."

  16. keebler01
    • 3 years ago
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    i wasright!!!!

  17. polpak
    • 3 years ago
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    No. Your answer and Alchemista's are different.

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