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Philosophy& 106 W09 Assignment 07
Name: I.B. Logician
Instructions: Fill in the answers on this assignment sheet, save it on your computer, and e-mail the completed assignment with your answers as e-mail text to the instructor by February 23, 2009. The reading
for Week Seven is section 8.4.
Use conditional proof, indirect proof, a combination of conditional and indirect proof, or direct proof (a proof without an assumption and just using the rules of inference) to derive the conclusions of the following
valid arguments. (8 points each)
1.
1. (Ex)Ax > (Ex)(Bx & Cx) 2. (Ex)(Cx v Dx) > (x)Ex /(x)(Ax>Ex)
3. Ax ACP
4. (Ex)Ax 3,EG
5. (Ex)Bx & Cx 1,4,MP
6. Ba & Ca 5,EI
7. Ca & Ba 6,com
8. Ca 7,simp
9. Ca v Da 8,add
10. (Ex)(Cx v Dx) 9,EG
11. (x)Ex 2,10,MP
12. Ex 11,UI
13. Ax > Ex 3-12,CP
14. (x)(Ax > Ex) 13,UG
2. 1. (Ex)Ax>(x)Bx
2. An>~Bn /~An
3. An AIP
4. ~Bn 2,3,MP
5. (Ex)Ax 3,EG
6. (x)Bx 1,5,MP
7. Bn 6,UI
8. Bn & ~Bn 4,7,conj
9. ~An 3-8,IP
3. 1. (x)[(Ax v Bx) > Cx] 2. (x)[(Cx v Dx) > ~Ax] /(x)~Ax
3. ~(x)~Ax AIP
4. (Ex)Ax 3,CQ
5. Am 4,EI
6. (Am v Bm)> Cm 1,UI
7. Am v Bm 5,add
8. Cm 6,7,MP
9. (Cm v Dm)> ~Am 2,UI
10. Cm v Dm 8,add
11. ~Am 9,10,MP
12. Am&~Am 5,11,conj
13. ~~(x)~Ax 3-12,IP
14. (x)~Ax 13,DN
4. (Hint: Use CP twice)
1. (x)[Ax > (Bx & Cx)]
2. (x)[Dx > (Ex & Fx)] /(x)(Cx > Dx) > (x)(Ax > Fx)
3. (x)(Cx > Dx) ACP
4. Ax ACP
5. Ax > (Bx & Cx) 1,UI
6. Bx & Cx 4,5,MP
7. Cx & Bx 6,com
8. Cx 7,simp
9. Cx > Dx 3,UI
10. Dx 8,9,MP
11. Dx > (Ex & Fx) 2,UI
12. Ex & Fx 10,11,MP
13. Fx & Ex 12,com
14. Fx 13,simp
15. Ax > Fx 4-14,CP
16. (x)(Ax > Fx) 15,UG 17. (x)Cx>Dx)>(x)(Ax>Fx) 3-16,CP
End of Assignment 07.
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