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keebler01

  • 3 years ago

Use De Morgan’s laws to determine whether the two statements are equivalent. ~ (p ∧ q), ~p ∧ ~q

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  1. joemath314159
    • 3 years ago
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    its been a while since ive dealt with truth tables and things like it, but when you negate something with a ^ or v in it, dont you switch it to the other?

  2. keebler01
    • 3 years ago
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    hold on im not sure let me look at me txt book!

  3. joemath314159
    • 3 years ago
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    i might be completely wrong, its been a while.

  4. joemath314159
    • 3 years ago
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    i think my book is in my car <.< im to tired to get it lol

  5. keebler01
    • 3 years ago
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    ~( p∧q)⇔~ p ∨ ~q by law 1 and this is not equivalent to ~ p ∧ ~ q, since if p is true and q is false, the first statement is true but the second is false. i got this from a website not sure if it correct!

  6. keebler01
    • 3 years ago
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    brb

  7. joemath314159
    • 3 years ago
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    i think thats right. I remember always having to switch the sign when you negate.

  8. joemath314159
    • 3 years ago
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    ima go get my book lol >.>

  9. keebler01
    • 3 years ago
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    ok

  10. keebler01
    • 3 years ago
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    im back!

  11. keebler01
    • 3 years ago
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    joe how would u write in ur own words?

  12. joemath314159
    • 3 years ago
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    if the problem didnt say "using De Morgan's Law", i would just use truth tables to show they arent equivalent.

  13. joemath314159
    • 3 years ago
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    but, since it say that, im looking through my book to see which Law would directly oppose that statement

  14. keebler01
    • 3 years ago
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    ok

  15. joemath314159
    • 3 years ago
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    alright i got it. i'll post a pic in a sec.

  16. SaltyPete
    • 3 years ago
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    by definition, the negation of (p ^ q) is (~p OR ~q), so they are not equivalent

  17. keebler01
    • 3 years ago
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    @ Joe i thnk i got it thanks!

  18. joemath314159
    • 3 years ago
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    ...and it looks like we arent able to post pics for the time being =/ bleh. Well, one of de Morgan's Laws is: \[\lnot(p\land q) \Leftrightarrow (\lnot p)\lor (\lnot q)\]

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