WEEK 5 :: Homework

Using ∃LOGIC construct annotated derivations showing that the following arguments are valid.


2:26 (P∨¬Q). (P→(V∧T)). ((¬V∨¬Q)→T) ∴ (R∨T)

2:27 (R∨T). (¬P↔(¬P→Q)) ∴ ((R∨S)∨(T∧Q))

2:28 (P→Q)∨(R→S) ∴ (P→S)∨(R→Q)

2:29 ¬(R↔S)↔(P→Q) ∴ (R↔¬S)↔(¬P∨Q)

2:30 (¬P∧¬Q)∨(¬¬R∧¬S). ¬(S∨Q). T→(¬S→¬R∧P) ∴ ¬T

2:31 (P∧Q)→((R∨S)∧¬(R∧S)). S→((R∧Q)∨(¬R∧¬Q)∨¬P). (R∧Q)→S ∴ (P→¬Q)

2:33 [T24] ∴ (P∧Q) ↔ (Q∧P)

2:34 [T25] ∴ P∧(Q∧R)↔(P∧Q)∧R

2:35 [T26] ∴ (P→Q)∧(Q→R)→(P→R)

2:36 [T27] ∴ ((P∧Q)→R)↔(P→(Q→R))

2:37 [T28] ∴ ((P∧Q)→R)↔((P∧¬R)→¬Q)

2:68 [T59] ∴ (P∨¬P)

2:74 [T65] ∴¬(P∧Q)↔(¬P∨¬Q) [complete without using dm]

   

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