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lgbasallote

  • 3 years ago

How many rows appear in a truth table for the compound proposition: \[(p \leftrightarrow q) \oplus (\neg p \leftrightarrow \neg r) \wedge \neg q\]

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  1. UnkleRhaukus
    • 3 years ago
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    you have three variables \(p,q,r\) so you will have \(2^3=8\) rows,

  2. UnkleRhaukus
    • 3 years ago
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    \[\begin{array}{|c|c|c|c|c|}\hline p& q&r&&\\\hline T&T&T&&\\T&T&F&&\\T&F&T&&\\ T&F&F&&\\F&T&T&&\\F&T&F&&\\F&F&T&&\\F&F&F&&\\\hline\end{array}\]

  3. lgbasallote
    • 3 years ago
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    so you ignore the negations?

  4. UnkleRhaukus
    • 3 years ago
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    \[\begin{array}{|c|c|c|c|c}\hline p&\neg p& q&\neg q&r&\neg r&\\\hline T&F&T&F&T&F\\T&F&T&F&F&T\\T&F&F&T&T&F\\ T&F&F&T&F&T\\F&T&T&F&T&F\\F&T&T&F&F&T\\F&T&F&T&T&F\\F&T&F&T&F&T\\\hline\end{array}\]

  5. UnkleRhaukus
    • 3 years ago
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    \[\begin{array}{|c|c|c|c|c|c|}\hline p&\neg p& q&\neg q&r&\neg r&p\iff q&\neg p\iff \neg q\\\hline T&F&T&F&T&F\\T&F&T&F&F&T\\T&F&F&T&T&F\\ T&F&F&T&F&T\\F&T&T&F&T&F\\F&T&T&F&F&T\\F&T&F&T&T&F\\F&T&F&T&F&T\\\hline\end{array}\]... to continue i need to know which has hight precedence in operation? \(\oplus,\lor\) ?

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