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Use your newly gained natural deduction skills to solve the following problems. In each problem, the arrow symbol means the same thing as the horseshoe symbol in the preceding chapter.1).1. F ∨ (D → T)2. ~F3. D/T2).1. P → (G → T)2. Q → (T → E)3. P4. Q/G → E3).1.~X → [~X → (Y → X)]2.~X /~Y4).1.K → (L → M)2.M ∨K3.~M /~L5).1. ~S→D2. ~S v (~D→K)3.~D/K

Respuesta :

varshamittal029

1. F v (D → T)

2.  V F

3. D

∴ T

4. D → T (Disjunctive syllogism 1,2)

5. T          ( Modus Ponens 3,4)

2. P → (cu → T)

2. Q → (T → E)

3. P

4. Q

∴ Cu → E

5. Cu → T  (modus ponens 1,3)

6. T → E  ( modus ponens 2,4)

7. Cu → E (Hypothetical syllogism 5,6)

3. 1. ~ X → [~X → (y → X)]

   2. ~ X

   ∴ ~ y

  3. ~X → (y → X)   (modus ponens 1,2)

  4.  y → X              ( modus ponens 2,3)

  5. ~ y                     ( modus tollens 2,4)

4. 1. k → (L→m)

    2. m v k

    3. ~m

    ∴ ~L

    4. K   (disjunctive syllogism 2,3)

    5. L → m  (modus ponens 1,4)

    6. ~ L    (modus tollens 3,5)

5. 1. ~S → D

   2. ~S v (~D→K)

   3. ~ D

∴ K

  4. ~(~S)   (Modulas tollens 1,3)

  5. S          ( Double nojection 4)

  6. ~D→K (Disjunctive syllogism 2,5)

  7. K         (Modus ponenes 3,6)

Hence we get the required answer.

Learn more about Natural deduction skills here:

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