1. Show that the following argument with hypotheses on lines 1-2 and conclusion on line c is valid using the rules of inference and logical equivalences. Clearly label each step. 1 p → q Premise 2 (r ∨ s) → (p ∧ ¬q) Premise . . . c ¬r Conclusion

From the premises ¬¬P ∨ Q, P ↔ R, and H → ¬Q derive H → P using the inference rules and equivalence lawsfrom the lectures. Start with the premises and state in each step which rule you are using. Following from this, Let¬¬P ∨ Q be true and H → ¬Q be true. Prove that H → P is true by contradiction.

Which of the following is the study of the principles of valid Inference and demonstration?Question 2Answera.Factb.Logicc.Ruled.Argument

Select the correct answerThe premises (p ∧ q) ∨ r and r → s imply which of the conclusion?Optionsp ∨ sp ∨ rp ∨ qq ∨ r

State whether each of the following propositions is a tautology or a contradiction or contingent (i.e. neither).You must give a (brief) reason to justify each of your answers.(a) P(b) (P ∧ Q) → (P → Q)(c) ¬(P → Q) → (¬Q)(d) (¬Q ∧ (P → Q)) → ¬P(e) ((P → Q) ∧ (Q → R)) ↔ (P → R)(f) (R ∨ P ) → (P ∨ (Q ∨ R))

Assume that all of the following are true(P ∨ Q) ⇒ RQ ∨ RR ⇒ PShow by contradiction that P is true.3