Project 2 Part 2 worth 50 points Spring 2025 1. Consider the following argument: Premises: ~p (r and ~s) t s u ~p ~w u or w Conclusion: ~t Use valid argument forms to deduce the conclusion from the premises. Give a reason for each step. 2. Consider the following argument: Premises: p q r or s ~s ~t ~q or s ~s (~p and r) u w or t Conclusion: u and w Use valid argument forms to deduce the conclusion from the premises. Give a reason for each step. 3. Prove the following logical equivalences. Do not use truth tables - instead use logical equivalencies from the notes and provide a reason for each step. a. p and (~q or p) = p b. ~(p or ~q) or (~p and ~q) = ~p 4. Simplify the following logical expression -- provide a reason for each step. ~((~p and q) or (~p and ~q)) or (p and q)