Determine the validity of the argument.

Question

I have this question and was hoping I could get some help on it:

p∧q∧r → s

u →s

p∧u∧~r

∴q

I have found: p is true u is true ~r is true r is false.

But I am unsure what to do to find the validity of the statement. My thinking is that premise 1 is (~p ∨ ~q ∨ ~r) ∨ s where S is true but I get stuck here.

Hopefully this made sense and thank you for your assistance!

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. — José Carlos Santos, Mar 24 '20 at 08:31
It's possible that $s$ just happens to be true even if none of $q$ is. There are conditions that make $s$ true but no conditions that make that make it false. You have know way of knowing if $q$ is true or not. — fleablood, Mar 26 '20 at 01:51

score 1 · Answer 1 · answered Mar 26 '20 at 01:38

No, $q$ does not follow. You can try it with $q$ both ways and see.

As you said, the third premise means $p$ is True, $u$ is True, and $r$ is False. Then the second premise means $s$ is True.

If $q$ is True, the first premise says $T \wedge T \wedge F \to T$, which is fine.

If $q$ is False, the first premise says $T \wedge F \wedge F \to T$, which is fine.

So we can conclude nothing about $q$.

Determine the validity of the argument.

1 Answers1