Mathematical Logic Proof (Notes)

Mathematical Logic Proof (Notes) - 11(A>E(E>A 10 ME...

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Proof for (AvB) v (C.D), (A<->E) . (B->F), K<-> ~(EvF), C-> B :. ~K 1) (AvB) V (C.D) 2) (A <-> E) . (B->F) 3) K <-> ~ (EvF) 4) C -> B 5) K Assume 6) [K-> ~(EvF)] . [~(E.F) ->K] 3, ME 7) K-> ~(EvF) 6, Simp 8) ~(E.F) 5,7 MP 9) ~E. ~F 8 Dem 10)A <-> E 2, Simp 11)(A->E) . (E->A)
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Unformatted text preview: 11)(A->E) . (E->A) 10, ME 12)A-> E 11, Simp 13)~E 9 Simp 14)~A 12, 13 MT 15)A v (Bv (C.D)) 1, As 16)B v (C.D) 14, 15 Ds 17) B->F 2, Simp 18)~F 9, Simp 19)~B 17, 18 MT 20)C.D 16,19 DS 21)~C 4, 19 MT 22)C 20, Simp 23)C. ~C 21,22 Conj...
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