Question $1[25$ Points$]$

Prove using natural deduction that the proposition $(pq{)}^{{?}^{?}}(pr)$ can be derived

from the proposition $p{q}^{{?}^{?}}r.$ In other words, take $p{q}^{{?}^{?}}r$ as a premise and

conclude $(pq{)}^{{?}^{?}}(pr)$ using natural deduction.

Question $2[15$ points $(8+7)$

You are given two propositional logic formulae. Identify whether they are correct

$($well$-$formed$)$ as per the grammar of propositional logic. If yes, provide an assignment

to the variables of that formula so that the formula evaluates to "False." If not, rewrite the

formula by changing exactly one symbol in the formula to anything of your choice so

that the formula becomes grammatically correct.

a$)(PvvQ)((R^{{?}^{?}}S)harr(TvvU))$

b$)(xY{)}^{{?}^{?}}(Zhar{r}^{{?}^{?}}W)vv(A^{{?}^{?}}B)$

Please do not use Chat GPT Otherwise i will report.