Philosophy 251: Handout #9

XVII. For each of the following arguments construct a derivation to prove that the argument is valid.

  1. A B, B ( C & D ), ~C v ~D / ~A
  2. ( J K ) & ~L, ( ~J  M ) v L, ( ~K M ) N / N
  3. ( V v W ) v ( X v Y ), ~W & ~( Y v V ) / X
  4. ~Z v ( ~A v ~B ), ( B & C ) v D, A / Z D
  5. E ( ~F v G ), I ( K & ~H ), ~( F & ~G ) I / E ( ~H & K )
  6. / J v ~J
  7. / M v [( ~M v N ) & ( ~M v O )]
  8. ( ~S & ~T ) v ( ~S & ~U ), ( W & X ) S / ~ W v ~X
  9. D ( ~E v F ), D E, ~( F v G ) / D H
  10. N ( O & ~P ), O ( R & S ), ~S v P / ~N
  11. [( X & Z ) & Y ] v ( ~X ~Y ), X Z, Z Y / X Y
  12. / [ C ( D & E )] [ ( ~D v ~E ) ~C ]
  13. / [ F v ( G v H )] [ H v ( G v F )]
  14. / [ ~P ( ~Q R )] [( P v Q ) v ( ~~Q v R )]
  15. / [ T v ( U W )] [ T v ( ~U ~W)]

 

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