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- #1

- Apr 13, 2013

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We suppose that the propositions $p,q$ are propositions such that the proposition $p \to q$ is false.

Find the truth values for each of the following propositions:

- $\sim q \to p$
- $p \land q$
- $q \to p$

I have thought the following:

Since the proposition $p \to q$ is false, either $p$ is true and $q$ is false, either $q$ is true and $p$ is false.

Thus, we have the following truth table:

$\begin{matrix}

p & q & \sim q & \sim q \to p & p \land q & q \to p\\

0 & 1 & 0 & 1 & 0 & 0\\

1 & 0 & 1 & 1 & 0& 0

\end{matrix}.$

So, $\sim q \to p$ is at each case $1$ since $\sim q$ and $p$ have the same values.

As for $p \land q$ it is always $0$ since $p$ and $q$ have different values.

$q \to p$ is for the same reason $0$.

Is everything right? Or am I somewhere wrong?