Write sentence in logic

Question

If it rains, he will be at home; otherwise he will go to the market or to school.

Let $p$ be rains, $q$ be at home, $m$ market, $s$ school

Is the correct statement

$p \implies q$? But what about $\neg p \implies m \lor s$?

Which one is correct or used?

Answer 1

You almost got it. You simply need to combine your two statements as follows: $$ (p \implies q) \wedge (\neg p \implies m \vee s). $$