Question

if p is true and ~ q is false, then p -> ~ q is false

Always
never
sometimes

Answer 1

i will make a truth table for you

Answer 2

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

\end{array}
}
$$

Answer 3

you can see in the right most column

Answer 4

so the negation of q is already negative right?

would it be always right? the q was just confusing me, i was wondering if i should follow the question about p being false or change it since it has ~ next to it .

Answer 5

what does that mean? there are 2 values. true and false, on and off
~T=F
~F=T

Answer 6

$$
\Huge{
\begin{array}{|l|c|r|c|l|} \hline
p&q&\neg q &p\to \neg q \\
\hline
T & T & F & \color{red}F \\ \hline
T& F & T& \color{red}T \\ \hline
F& T & F& \color{red}T \\ \hline
F& F & T& \color{red}T \\ \hline

\end{array}
}

$$

Answer 7

we see that in the right column in red, \( \Large { p \to \neg q } \) is not always false.

Answer 8

there are actually 4 cases to consider
p = True , ~q = True
p = True , ~q = False
p = False , ~q = True
p = False , ~q = False

but the truth table makes finding it easier

Answer 9

I think the existence of t he q column was throwing them off. You only have to focus on the p and ~q columns.

then recall that p->q is true for
TT,FT,FF

Answer 10

thanks guys i understand now ~