## lgbasallote 3 years ago How many rows appear in a truth table for the compound proposition: $(p \leftrightarrow q) \oplus (\neg p \leftrightarrow \neg r) \wedge \neg q$

1. UnkleRhaukus

you have three variables $$p,q,r$$ so you will have $$2^3=8$$ rows,

2. UnkleRhaukus

$\begin{array}{|c|c|c|c|c|}\hline p& q&r&&\\\hline T&T&T&&\\T&T&F&&\\T&F&T&&\\ T&F&F&&\\F&T&T&&\\F&T&F&&\\F&F&T&&\\F&F&F&&\\\hline\end{array}$

3. lgbasallote

so you ignore the negations?

4. UnkleRhaukus

$\begin{array}{|c|c|c|c|c}\hline p&\neg p& q&\neg q&r&\neg r&\\\hline T&F&T&F&T&F\\T&F&T&F&F&T\\T&F&F&T&T&F\\ T&F&F&T&F&T\\F&T&T&F&T&F\\F&T&T&F&F&T\\F&T&F&T&T&F\\F&T&F&T&F&T\\\hline\end{array}$

5. UnkleRhaukus

$\begin{array}{|c|c|c|c|c|c|}\hline p&\neg p& q&\neg q&r&\neg r&p\iff q&\neg p\iff \neg q\\\hline T&F&T&F&T&F\\T&F&T&F&F&T\\T&F&F&T&T&F\\ T&F&F&T&F&T\\F&T&T&F&T&F\\F&T&T&F&F&T\\F&T&F&T&T&F\\F&T&F&T&F&T\\\hline\end{array}$... to continue i need to know which has hight precedence in operation? $$\oplus,\lor$$ ?