# Thread: A rules of inference question

1. ## A rules of inference question

This might be easy for some, but I seem to be having a bit of trouble grasping the concepts behind rules of inference.

Given the premises “if it doesn’t snow or if the roads are clear, then I will drive to Montreal and visit my sister,” “if I drive to Montreal, I can visit a museum,” and “I do not visit a museum,” use the rules of inference to determine whether or not “It snowed” is a valid conclusion.

2. Originally Posted by Runty
Given the premises “if it doesn’t snow or if the roads are clear, then I will drive to Montreal and visit my sister,” “if I drive to Montreal, I can visit a museum,” and “I do not visit a museum,” use the rules of inference to determine whether or not “It snowed” is a valid conclusion.
Forget the sister bit. It has nothing to do with question.
$\begin{array}{*{20}c}
{\left( {\neg S \vee C} \right) \to M} \\
{M \to V} \\
{\neg V} \\
\hline
{\neg M} \\
{S \wedge \neg C} \\
S \\ \end{array}$

Now you supply reasons.

3. Originally Posted by Plato
Forget the sister bit. It has nothing to do with question.
$\begin{array}{*{20}c}
{\left( {\neg S \vee C} \right) \to M} \\
{M \to V} \\
{\neg V} \\
\hline
{\neg M} \\
{S \wedge \neg C} \\
S \\ \end{array}$

Now you supply reasons.
That does help a bit, but I could use a bit more detail (these rules are a bit difficult to wrap my head around). Does your answer show that the conclusion is valid or invalid?

4. It snowed is valid.
We use modus tollens twice.
Then simplification.