Proofs Using RPI, RR, CP, and TI
Directions: Complete 10 of the 11 following proofs using the Rules of Proper Inference
and the Rules of Replacement. You may also elect to construct a Conditional Proof or
Indirect Proof.
(1) Prove: E ⊃ M
[#] [#] (#) Premise or Inference # # # RPI or RR
(1) A ⊃ (E ⊃ ∼F) P
(2) H ∨ (∼F ⊃ M) P
(3) A P
(4) ∼H P
(5)
(6)
(7)
(8)
(9)
(2) Prove: ∼P
[#] [#] (#) Premise or Inference # # # RPI or RR
(1) (L ≡ N) ⊃ C P
(2) (L ≡ N) ∨ (P ⊃ ∼E) P
(3) ∼E ⊃ C P
(4) ∼C P
(5)
(6)
(7)
(8)
(9)
(10)
(3) Prove: A ⊃ K
[#] [#] (#) Premise or Inference # # # RPI or RR
(1) (B ∨ F) ⊃ (A ⊃ G) P
(2) (B ∨ E) ⊃ (G ⊃ K) P
(3) B • ∼H P
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(4) Prove: G
[#] [#] (#) Premise or Inference # # # RPI or RR
(1) (∼K • ∼N) ⊃ [(∼P ⊃ K)•(∼R ⊃ G)] P
(2) K ⊃ N P
(3) ∼N • B P
(4) ∼P ∨ ∼R P
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(5) Prove: ∼S • ∼J
[#] [#] (#) Premise or Inference # # # RPI or RR
(1) ∼(J ∨ K) P
(2) B ⊃ K P
(3) S ⊃ B P
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(6) Prove: ∼D
[#] [#] (#) Premise or Inference # # # RPI or RR
(1) ∼(F • A) P
(2) ∼(L ∨ ∼A) P
(3) D ⊃ (F ∨ L) P
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
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