Answer to Question #129751 in Discrete Mathematics for gazal

Question

Determine whether the conclusion C is valid in the following premises without
using truth table: H1: ¬Q, H2: P → Q, C: ¬ P

Answer 1

Since rule of contraposition $(P\to Q)\to(\neg Q\to\neg P)$ is valid, we have that $\neg Q\to\neg P$ is valid if $P\to Q$ is valid. And if $\neg Q\to\neg P$ and $\neg Q$ are valid, then $\neg P$ is valid.

So we obtain that $\neg P$is valid if $P\to Q$ and $\neg Q$ are valid.

Answer: $C$ is valid in premises $H1$ and $H2$.