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lgbasallote Group Title

Evaluate: \[[\neg p \wedge (p \vee q)] \rightarrow q\]

  • 2 years ago
  • 2 years ago

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  1. lgbasallote Group Title
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    i suppse \[\neg p \wedge (p \vee q) \equiv p\]

    • 2 years ago
  2. lgbasallote Group Title
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    so then it becomes \[p \rightarrow q\]

    • 2 years ago
  3. lgbasallote Group Title
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    then what?

    • 2 years ago
  4. lgbasallote Group Title
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    oh i see

    • 2 years ago
  5. lgbasallote Group Title
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    i made a mistake

    • 2 years ago
  6. lgbasallote Group Title
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    \[\neg p \wedge (p \vee q) \equiv F \vee (\neg p \wedge q) \rightarrow q\]

    • 2 years ago
  7. lgbasallote Group Title
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    then this becomes \[T \wedge (p \vee q) \vee q\]

    • 2 years ago
  8. lgbasallote Group Title
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    then \[T \wedge (p \vee q) \equiv p \vee q \]

    • 2 years ago
  9. lgbasallote Group Title
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    in my solution i will be treating them the same....my latex is gonna get confusing if i follow the rules

    • 2 years ago
  10. lgbasallote Group Title
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    \[\equiv p \vee q \vee q\] \[q \vee q \equiv T\] so.. \[\equiv p \vee T \equiv T\] yes?

    • 2 years ago
  11. lgbasallote Group Title
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    so then this is a tautology?

    • 2 years ago
  12. PhoenixFire Group Title
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    implication law is P->Q=nP V Q Right? Sorry for no Latex,

    • 2 years ago
  13. lgbasallote Group Title
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    yes

    • 2 years ago
  14. lgbasallote Group Title
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    so is that a yes to my question?

    • 2 years ago
  15. PhoenixFire Group Title
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    yes it's a tautology, but you messed something up and somehow ended up with a tautology anyways lol

    • 2 years ago
  16. lgbasallote Group Title
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    where?

    • 2 years ago
  17. UnkleRhaukus Group Title
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    \[\small¬p∧(p∨q)\Rightarrow q\iff(\neg p\wedge p) \vee(\neg p\lor q)\Rightarrow q\iff (\neg p\lor q)\Rightarrow q \iff (\neg p\Rightarrow q)\vee(q\Rightarrow q )\]\[\iff q\Rightarrow q\qquad \top\]

    • 2 years ago
  18. lgbasallote Group Title
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    hmm looks different...

    • 2 years ago
  19. lgbasallote Group Title
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    implication is distributive?

    • 2 years ago
  20. PhoenixFire Group Title
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    • 2 years ago
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  21. lgbasallote Group Title
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    seems you're the one who went wrong @PhoenixFire ....

    • 2 years ago
  22. lgbasallote Group Title
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    \[(\neg p \wedge q) \rightarrow q\] should become \[\neg(\neg p \wedge q) \vee q\] by DM law \[p \vee q \vee q\]

    • 2 years ago
  23. lgbasallote Group Title
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    hmm seems i missed a step too

    • 2 years ago
  24. lgbasallote Group Title
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    nevertheless, important thing is.. i was right....that was my question in the first place anyways

    • 2 years ago
  25. PhoenixFire Group Title
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    de morgans law.... you have to negate both. n(nP ^ Q) V Q becomes nnP V nQ V Q

    • 2 years ago
  26. PhoenixFire Group Title
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    nnP <-- Involution law becomes P. What you missed was distributing the negative to the Q during De Morgan's Law

    • 2 years ago
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