1. [10] In all of the following, lines 1 and 2 are premises. In which of the five is line 3 correctly derived as specified by the included justification? (There may be more than one correct answer.)[ ] A1. A ⊃ B2. B3.A 1,2 MT[ ] B1. A ⊃ B2. C3.A • C 1,2 Conj[ ] C1. A ⊃ B2. A3.C v (A ⊃ B) 1 DI[ ] D1. A • B2. C • (D • F)3. D • F 2,Simp[ ] E1. A ⊃ ~(B v C)2. ~A3.B v C 1,2 MP2. [10] Which of the following is/are TRUE? (There may be more than one correct answer.)[ ] A. If any premises in an argument is a contradiction, then the argument is valid.[ ] B. If the conclusion of an argument is a tautology, then the argument is valid.[ ] C. If all premises in an argument are consistent, then the argument is valid.[ ] D. If each premise in an argument is equivalent to the conclusion, then the argument is valid.[ ] E. If the premises in an argument are inconsistent, then the argument is invalid.3. [10] Fill in the justifications1. ~(~C • ~D) ⊃ ~(A • B)2.F •B3.A • E / ∴ ~C v (F ⊃ E)4.A 5.B 6. A • B 7. ~C • ~D 8. ~C 9.~ C v (F ⊃ E) 4. [10] Fill in the derived lines1. X2. ~[X ⊃ (~Z ⊃Y)] ⊃ ~X3.~X v ~Z / ∴(Z ⊃ Y) v Y4. 1,2 MT5. 1,4 MP6. 1,3 DS7. 5,6 MP8. 7 DIFor Problems 5 and 6, do the proof using only MP, MT, DS, DI, Simp and Conj5. [15]1. C v ~G2. (X v G) ⊃ ~C3. X / ∴ ~G v M6. [15]1. ~A2. (~F v G) ⊃ (A v I)3. F ⊃ A / ∴ ~F • IFor problems 7 and 8, do the indicated proof using only MP, MT, DS, DI, Simp and Conj, and you may also use conditional proof if desired.7. [15]1. ~(K ⊃ G) ⊃ ~Y2. Y3. ~ (G ⊃ B) ⊃ ~Z4. Z /∴ K ⊃ B8. [15]1. B v ~E2. Y ⊃ B3. ~L ⊃ ~B4. ~B v K / ∴ (Y ⊃ K) • (E ⊃ L)Question: Do this proof WITHOUT using DI. (Hint: try conditional proof and dilemma)1. ~(X ⊃ X) v (Z v Y)2. Y ⊃ A3. ~Z v B /∴ A v B