$$ \begin{array}{l} 1.\>\>\>\> (r ∧ ¬s) ∨ (q ∧ ¬s)\\ 2.\>\>\>\> ¬s → ((p ∧ r) → u)\\ 3.\>\>\>\> u → (s ∧ ¬t)\\ \dfrac{\quad\qquad\qquad\qquad\qquad\qquad}{\text{Prove from the previous arguments. }\quad p → q} \end{array} $$
Hey guys, I am really lost, so far I have a few arguments but not sure if they're correct. Can you please give some arguments to get this solved or a game plan using Inference laws and equivalences. Inferences: Modus Ponens, Tollens, Hypothetical, Disjunctive, Resolution, Conjunction, Simplification, Addition.
This is what I have so far.... 4. (r ∨ q) ∧ ¬s Distributive of 1 5. ¬s Simplification of 1 6. (p ∧ r) → u Modus Ponens of 2 7. ¬u Modus Tollens of 3 8. ¬(p ∧ r) Modus tollens 9. p → ¬r DeMorgans and Implication Definition\ 10. (r ∨ q) Simplification 11. ( ¬r → q) Implication 12. p → q Hypothetical
Are these steps valid?