Question

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

Give a step-by-step argument using valid Rules of Inference

Answer 1

If it is a wild animal then it is dangerous,

$$(P\to Q)$$

If it is dangerous it will hurt you,

$$(Q\to R)$$

By hypothetical syllogism,

$$(P\to R)$$

By modulus tollens,

$$(P\to R),\neg R$$

$$\neg P$$