SOLVED LOGIC PROBLEMS 1 |(x)(Fx & Gx) / (x)Fx +--------------------- 2 |Fa & Ga 1,UE 3 |Fa 2,&E 4 |(x)Fx 3,UI SET C PROB A 1 |(x)(Mx > Nx) P 2 |(x)Mx / (x)Nx +--------------------- 3 |Ma > Na 1,UE 4 |Ma 2,UE 5 |Na 3,4,>E 6 |(x)Nx 5,UI SET C PROB B 1 |A / (x)(A v Nx) +--------------------- 2 |A v Na 1,vI 3 |(x)(A v Nx) 2,UI SET C PROB C 1 |(x)Hx & (x)Qx / (x)(Hx & Qx) +--------------------- 2 |(x)Hx 1,&E 3 |(x)Qx 1,&E 4 |Ha 2,UE 5 |Qa 3,UE 6 |Ha & Qa 4,5,&I 7 |(x)(Hx & Qx) 6,UI SET C PROB D 1 |(x)(Kxm & Kmx) / (x)Kxm & (x)Kmx +--------------------- 2 |Kam & Kma 1,UE 3 |Kam 2,&E 4 |Kma 2,&E 5 |(x)Kxm 3,UI 6 |(x)Kmx 4,UI 7 |(x)Kxm & (x)Kmx 5,6,&I SET C PROB E 1 |(x)(Fx v Gx) P 2 |(x)(Fx > Gx) / (x)Gx +--------------------- 3 |Fa v Ga 1,UE 4 |Fa > Ga 2,UE 5 | |Ga A | +--------------------- 6 | |Ga 5,R 7 |Ga > Ga 5-6,>I 8 |Ga 3,AC 9 |(x)Gx 8,UI SET C PROB F 1 |(x)~Px v C / (x)(~Px v C) +--------------------- 2 | |(x)~Px A | +--------------------- 3 | |~Pa 2,UE 4 | |~Pa v C 3,vI 5 | 6 | |C A | +--------------------- 7 | |~Pa v C 6,vI 8 | 9 |~Pa v C 1,2-4,6-7,AC 10 |(x)(~Px v C) 9,UI SET C PROB G 1 |(x)(Rxb > Rax) / (x)Rxb > (x)Rax +--------------------- 2 | |(x)Rxb A | +--------------------- 3 | |(x)(Rxb > Rax) 1,R 4 | |Rcb 2,UE 5 | |Rcb > Rac 3,UE 6 | |Rac 4,5,>E 7 | |(x)Rax 6,UI 8 |(x)Rxb > (x)Rax 2-7,>I SET C PROB H 1 |(x)(Gxh > Gxm) / (x)(~Gxm > ~Gxh) +--------------------- 2 | |~Gam A | +--------------------- 3 | |(x)(Gxh > Gxm) 1,R 4 | |Gah > Gam 3,UE 5 | |~Gah 2,4,DC 6 |~Gam > ~Gah 2-5,>I 7 |(x)(~Gxm > ~Gxh) 6,UI SET C PROB I 1 |(x)(Mx > Nx) P 2 |(x)(Nx > Ox) / (x)(Mx > Ox) +--------------------- 3 | |Ma A | +--------------------- 4 | |(x)(Mx > Nx) 1,R 5 | |(x)(Nx > Ox) 2,R 6 | |Ma > Na 4,UE 7 | |Na > Oa 5,UE 8 | |Na 3,6,>E 9 | |Oa 8,7,>E 10 |Ma > Oa 3-9,>I 11 |(x)(Mx > Ox) 10,UI SET C PROB J 1 |T > (x)Mdx / (x)(T > Mdx) +--------------------- 2 | |T A | +--------------------- 3 | |T > (x)Mdx 1,R 4 | |(x)Mdx 2,3,>E 5 | |Mdc 4,UE 6 |T > Mdc 2-5,>I 7 |(x)(T > Mdx) 6,UI SET C PROB K 1 |(x)(Sx ­ Ox) / (x)Sx ­ (x)Ox +--------------------- 2 | |(x)Sx A | +--------------------- 3 | |(x)(Sx ­ Ox) 1,R 4 | |Sa 2,UE 5 | |Sa ­ Oa 3,UE 6 | |Oa 4,5,­E 7 | |(x)Ox 6,UI 8 | 9 | |(x)Ox A | +--------------------- 10 | |(x)(Sx ­ Ox) 1,R 11 | |Sa ­ Oa 10,UE 12 | |Oa 9,UE 13 | |Sa 11,12,­E 14 | |(x)Sx 13,UI 15 | 16 |(x)Sx ­ (x)Ox 2-7,9-14,­I SET C PROB L 1 |(x)(Hff > Lxx) / Hff > (x)Lxx +--------------------- 2 | |Hff A | +--------------------- 3 | |(x)(Hff > Lxx) 1,R 4 | |Hff > Lss 3,UE 5 | |Lss 2,4,>E 6 | |(x)Lxx 5,UI 7 |Hff > (x)Lxx 2-6,>I SET C PROB M 1 |(x)Px v (x)Qx / (x)(Px v Qx) +--------------------- 2 | |(x)Px A | +--------------------- 3 | |Pa 2,UE 4 | |Pa v Qa 3,vI 5 | |(x)(Px v Qx) 4,UI 6 | 7 | |(x)Qx A | +--------------------- 8 | |Qa 7,UE 9 | |Pa v Qa 8,vI 10 | |(x)(Px v Qx) 9,UI 11 | 12 |(x)(Px v Qx) 1,2-5,7-10,AC SET C PROB N 1 |(x)Hx P 2 |(Ex)Hx > (x)(Hx > Jx) / (x)Jx +--------------------- 3 |Ha 1,UE 4 |(Ex)Hx 3,EI 5 |(x)(Hx > Jx) 2,4,>E 6 |Ha > Ja 5,UE 7 |Ja 3,6,>E 8 |(x)Jx 7,UI SET C PROB O 1 |(Ex)Px > A / (x)(Px > A) +--------------------- 2 | |Pa A | +--------------------- 3 | |(Ex)Px 2,EI 4 | |(Ex)Px > A 1,R 5 | |A 3,4,>E 6 |Pa > A 2-5,>I 7 |(x)(Px > A) 6,UI SET C PROB P 1 |~(Ex)Px / (x)~Px +--------------------- 2 | |Pa A | +--------------------- 3 | |~(Ex)Px 1,R 4 | |(Ex)Px 2,EI 5 |~Pa 3,4,(2-4),~I 6 |(x)~Px 5,UI SET C PROB Q 1 |~(x)(Jx > ~Kx) / (Ex)(Jx & Kx) +--------------------- 2 | |~(Ex)(Jx & Kx) A | +--------------------- 3 | | |Ja A | | +--------------------- 4 | | | |Ka A | | | +--------------------- 5 | | | |Ja 3,R 6 | | | |Ja & Ka 4,5,&I 7 | | | |(Ex)(Jx & Kx) 6,EI 8 | | | |~(Ex)(Jx & Kx) 2,R 9 | | |~Ka 7,8,(4-8),~I 10 | |Ja > ~Ka 3-9,>I 11 | |(x)(Jx > ~Kx) 10,UI 12 | |~(x)(Jx > ~Kx) 1,R 13 |~~(Ex)(Jx & Kx) 11,12,(2-12),~I 14 |(Ex)(Jx & Kx) 13,~E SET C PROB R 1 |(x)Px > A / (Ex)(Px > A) 17 | |A 15,16,>E +--------------------- 18 | | |Pb A 2 | |~(Ex)(Px > A) A | | +--------------------- | +--------------------- 19 | | |A 17,R 3 | | |~Pb A 20 | |Pb > A 18-19,>I | | +--------------------- 21 | |(Ex)(Px > A) 20,EI 4 | | | |Pb A 22 | |~(Ex)(Px > A) 2,R | | | +--------------------- 23 |~~(Ex)(Px > A) 21,22,(2-22),~I 5 | | | | |~A A 24 |(Ex)(Px > A) 23,~E | | | | +--------------------- 6 | | | | |~Pb 3,R 7 | | | | |Pb 4,R 8 | | | |~~A 6,7,(5-7),~I 9 | | | |A 8,~E 10 | | |Pb > A 4-9,>I 11 | | |(Ex)(Px > A) 10,EI 12 | | |~(Ex)(Px > A) 2,R 13 | |~~Pb 11,12,(3-12),~I 14 | |Pb 13,~E 15 | |(x)Px 14,UI 16 | |(x)Px > A 1,R SET C PROB S 1 |~(x)Px / (Ex)~Px +--------------------- 2 | |~(Ex)~Px A | +--------------------- 3 | | |~Pa A | | +--------------------- 4 | | |(Ex)~Px 3,EI 5 | | |~(Ex)~Px 2,R 6 | |~~Pa 4,5,(3-5),~I 7 | |Pa 6,~E 8 | |(x)Px 7,UI 9 | |~(x)Px 1,R 10 |~~(Ex)~Px 8,9,(2-9),~I 11 |(Ex)~Px 10,~E SET C PROB T 1 |~(Ex)Qx v H / (x)(~Qx v H) +--------------------- 2 | |H A | +--------------------- 3 | |~Qa v H 2,vI 4 | 5 | |~(Ex)Qx A | +--------------------- 6 | | |Qa A | | +--------------------- 7 | | |(Ex)Qx 6,EI 8 | | |~(Ex)Qx 5,R 9 | |~Qa 7,8,(6-8),~I 10 | |~Qa v H 9,vI 11 | 12 |~Qa v H 1,2-3,5-10,AC 13 |(x)(~Qx v H) 12,UI SET C PROB U 1 |~(Ex)Dx / (x)(Dx > Kx) +--------------------- 2 | |Da A | +--------------------- 3 | | |~Ka A | | +--------------------- 4 | | |Da 2,R 5 | | |(Ex)Dx 4,EI 6 | | |~(Ex)Dx 1,R 7 | |~~Ka 5,6,(3-6),~I 8 | |Ka 7,~E 9 |Da > Ka 2-8,>I 10 |(x)(Dx > Kx) 9,UI SET C PROB V