Exercise

Construct proofs for the following valid arguments. The first fifteen proofs can be complete in three or less additional lines. The next five proofs will be a bit longer. It is important to note that there is always more than one way to construct a proof. If your proof differs from the answer key, that doesn't mean it is wrong. #1


    1. A ⋅ B
    2. (A v C) ⊃ D /∴ A ⋅ D
  2.  
    1. A
    2. B /∴ (A v C) ⋅ B

    1. D ⊃ E
    2. D ⋅ F /∴ E

    1. J ⊃ K
    2.  J /∴ K v L

    1. A v B
    2. ~A ⋅ ~C /∴ B

    1. A ⊃ B
    2. ~B ⋅ ~C /∴ ~A

    1. D ⊃ E
    2. (E ⊃ F) ⋅ (F⊃ D) /∴D ⊃ F

    1. (T ⊃ U) ⋅ (T ⊃ V)
    2. T /∴ U v V

    1. (E ⋅ F) v (G ⊃ H)
    2. I ⊃ G
    3. ~(E ⋅ F) /∴ I ⊃ H

    1. M ⊃ N
    2. O ⊃ P
    3. N ⊃ P
    4. (N ⊃ P) ⊃ (M v O) /∴N v P

    1. A v (B ⊃ A)
    2. ~A ⋅ C /∴ ~B

    1. (D v E) ⊃ (F ⋅ G)
    2. D /∴ F

    1. T ⊃ U
    2. V v ~U
    3. ~V ⋅ ~W /∴ ~T

    1. (A v B) ⊃ ~C
    2. C v D
    3. A /∴ D

    1. L v (M ⊃ N)
    2. ~L ⊃ (N ⊃ O)
    3. ~L /∴ M ⊃ O

    1. A ⊃ B
    2. A v (C ⋅ D)
    3. ~B ⋅ ~E /∴ C

    1. (F ⊃ G) ⋅ (H ⊃ I)
    2. J ⊃ K
    3. (F v J) ⋅ (H v L) /∴ G v K

    1. (E v F) ⊃ (G ⋅ H)
    2. (G v H) ⊃ I
    3. E /∴ I

    1. (N v O) ⊃ P
    2. (P v Q) ⊃ R
    3. Q v N
    4. ~Q /∴ R

    1. J ⊃ K
    2. K v L
    3. (L ⋅ ~J) ⊃ (M ⋅ ~J)
    4. ~K    /∴ M