Question

Use a truth table to determine whether the argument given below is valid:
If it is a wild animal, it is dangerous. If it is dangerous, it will hurt
you. However, it is not dangerous. Therefore, it is not a wild animal.

Answer 1

Logical statements:

If it is a wild animal, it is dangerous. If it is dangerous, it will hurt you. However, it is not dangerous. Therefore, it is not a wild animal.

Let's denote all the expressions:

w - it is a wild animal

d - it is dangerous

h - it will hurt you

Then the logical chain is such:

w->d

d->h

$\neg d$

Conclusion: $\neg w$

Truth table for $w\to d$

Since the only row where $d = \text{FALSE}$ contains $w = \text{FALSE}$ this logical chain implies $\neg w$ , so the argument is valid.