pracanswers3 - Introduction to Logic Practice Exam 3...

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Introduction to Logic — Practice Exam 3 Answers 1. I n & I j 2. Gn & Gm or ( Gn Gm ) 3. Nnu 4. Ocn Oc j 5. x ( Sx → ∼ I x ) or ∼∃ x ( Sx & I x ) 6. x ( P x & I x ) or ∼∀ x ( P x I x ) 7. x [( Gx & P x ) Rx ] 8. ∼∀ x I x or x I x 9. x ( Rx & Gx ) 10. x [( Gx & P x ) ( Rx Dx )] 11. x Gx → ∀ x P x or ∼∀ x P x → ∼∀ x Gx or x P x → ∼∀ x Gx or x Gx → ∼∃ x P x 12. x [( P x Sx ) ( I x Gx )] or x [ P x ( I x Gx )] & x [ Sx ( I x Gx )] 13. (Among everything, only inhabitable planets rotate.) x [ ( I x & P x ) → ∼ Rx ] or x [ Rx ( I x & P x )] (Among planets, only the inhabitable ones rotate.) x [ ( I x & P x ) → ∼ ( Rx & P x )] or x [( Rx & P x ) ( I x & P x )] or x [( Rx & P x ) I x ] or x [ P x ( Rx I x )] or x [ P x ( I x → ∼ Rx )] etc. 14. x [( Gx & P x ) Rx ] or x [ Rx → ∼ ( Gx & P x )] 15. x ( P x I x ) → ∃ x [( Gx & P x ) & I x ] 16. I j → ∀ x [( I x & P x ) → ∼ Gx ] or I j → ∼∃ x [( I x & P x ) & Gx ] or ∼∃ x [( I x & P x ) & Gx ] I j or x [( I x & P x ) → ∼ Gx ] I j etc. 17. x Ox j 18. x Ox j or ∼∀ x Ox j 19. x y Oyx 20. x y Oxy or x ∼∃ y Oxy 21. x ( Ox j Lj x ) 22. x ( Lxm & Ox j ) 23. x (
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