If English then logic
Wednesday, 14 December 2011
Logic and Philosophy, A. Hausman, H. Kahane, P. Tidman, Wadsworth, 11th ed., 2010, 13-1(2)
Prove valid:
(x)(Px
⊃ Qx)
(x)(Qx
⊃ Rx)
Pa
•
¬ Rb
∴
a
≠ b
Pa
⊃ Qa ......... 1 UI x/a
Pa ......... 3 Simp.
Qa ......... 5,6 MP
Qa
⊃ Ra ......... 2 UI x/a
Ra ......... 7,8 MP
¬ Rb ......... 3 Simp.
a
≠ b ......... 9,10 Id
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