Which of the following are correct applications of the transformation rule cited? Say Correct or Incorrect. Remember that the order of the premises does not matter.(A V ~B) ⊃ ~C, (A V ~B) /:. C --> MP INCORRECT ~(A V B) ⊃ C, ~C / :. ~(A V B) --> MT INCORRECT~A ⊃ ~(B V C), (D & E) ⊃ ~A / :. (D & E) ⊃ ~(B V C) --> HS CORRECT ~B / :. (~A & (~D ⊃ (C& ~E))) V ~B --> Add. CORRECT~(A V B) V (C ⊃ ~D), ~(C⊃ ~D) / :. ~(A V B) --> DS CORRECT 2. Cite the transformation rule that was used in the following valid inferences.(~A V ~B) V C, ~C /:. ~A V ~B – Disjunctive Syllogism ~(A V B) ⊃ (~A V ~B), ~(~A V ~B) / :. ~~(A V B) Modus Tollens (denying the consequent) (~B V ~C) ⊃ ~D, ~A ⊃ (~B V ~C) / :. ~A ⊃ ~D Hypothetical Syllogism ~(~B ⊃ ~A), A ⊃ (~B ⊃ ~A) / :. ~A Modus Tollens (~B ⊃ ~C) ⊃ (~A ⊃ ~B), ~A ⊃ (~B ⊃ ~C)/ :. ~A ⊃ (~B ⊃ ~C) Repetition 3. Using the transformation rules of system P, prove each of the following arguments to be valid:(B ⊃ ~A), (C ⊃ B), A /:. ~C 1. (B ⊃ ~A) Premise 12. (C ⊃ B) Premise 2 3. A Premise 3 4. C ⊃ ~A HS, 1,2 5. ~~A DN, 36. ~C MT, 4,5 (A V ~B), (~C V B), ~A / :. ~C1. (A V ~B) Premise 12. (~C V B) Premise 2 3. ~A Premise 3 4. ~B DS, 1,35. ~C DS, 2,4 (A V B) ⊃ ~C, (C V D), A / :. D1. (A V B) ⊃ ~C Premise 1 2. (C V D) Premise 2 3. A Premise 3 4. (A V B) Addition 35. ~C MP 1,4