Rule of inference proof

Question

"Either I go to library or if I wait for my mom then I have to go to the party."
"I will go to the party if I meet my friends"
"If I go to the library then I will finish my homework."
"I did not finish my homework."

Use the rule of inference to prove the theorem:
"If I wait for my mom then I will meet my friends"

Note:

• The first rule is $p \lor (q \rightarrow r)$
• The second premise..I don't know how to convert..can anyone help?

Answer 1

Hint

You have to corrcetlly formalize the different statements :

$p$ is "I go to library"

$q$ is "I wait for my mom"

$r$ is "I go to the party"

$s$ is "I meet my friends"

$t$ is "I finish my homework".

Now we have to correctly express the premises of the argument :

1) $p \lor (q \to r)$

2) $s \to r$

3) $p \to t$

4) $\lnot t$.

Finally, the sought conclusion :

5) $q \to s$.