Wednesday, 14 December 2011

Logic and Philosophy, A. Hausman, H. Kahane, P. Tidman, Wadsworth, 11th ed., 2010, 13-1(2)

Prove valid:
  1. (x)(Px ⊃ Qx)
  2. (x)(Qx ⊃ Rx)
  3. Pa ¬ Rb
  4. a ≠ b
  5. Pa ⊃ Qa ......... 1 UI x/a
  6. Pa ......... 3 Simp.
  7. Qa ......... 5,6 MP
  8. Qa ⊃ Ra ......... 2 UI x/a
  9. Ra ......... 7,8 MP
  10. ¬ Rb ......... 3 Simp.
  11. a ≠ b ......... 9,10 Id

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