Question

(a)
\[\begin{array}{|c|c|c|c|c|}\hline\phi &\psi &\phi\Rightarrow\psi&\phi\wedge(\phi\Rightarrow\psi)&[\phi\wedge(\phi\Rightarrow\psi)]\Rightarrow\psi\\ \hline T&T &T&T&T\\ T&F&F&F&T\\ F&T&T&F&T\\F&F&T&F&T \\ \hline \end{array}\]

(b)
\[\text{The truth table demonstrates that for any value of \(\phi,\psi\)}\]
\[\text{{Modus ponens}; \(\quad\) if \(\phi \Rightarrow \psi\) and you know \(\phi\), then \(\psi\) is always true.}\]

Answer 1

what do you think

Answer 2

Edit the q " and you know \[\phi = T\] '

Answer 3

pardon?

Answer 4

do i only need the first two rows?

Answer 5

Well, to be precise , you need them all. But when in \[F\wedge whatever = F\] and then using it
\[(F\Rightarrow anything) = T\]