SOLVED LOGIC PROBLEMS 1 |(Ex)Lxx / (Ex)(Ey)Lxy +--------------------- 2 |a|Laa A | +--------------------- 3 | |(Ey)Lay 2,EI 4 | |(Ex)(Ey)Lxy 3,EI 5 |(Ex)(Ey)Lxy 1,2-4,EE SET E PROB A 1 |(x)(y)Lxy / (x)Lxx +--------------------- 2 |(y)Lay 1,UE 3 |Laa 2,UE 4 |(x)Lxx 3,UI SET E PROB B 1 |(x)(y)Lxy / (y)(x)Lxy +--------------------- 2 |(y)Lay 1,UE 3 |Lab 2,UE 4 |(x)Lxb 3,UI 5 |(y)(x)Lxy 4,UI SET E PROB C 1 |(Ex)(Ey)Lxy / (Ey)(Ex)Lxy +--------------------- 2 |a|(Ey)Lay A | +--------------------- 3 | |b|Lab A | | +--------------------- 4 | | |(Ex)Lxb 3,EI 5 | | |(Ey)(Ex)Lxy 4,EI 6 | |(Ey)(Ex)Lxy 2,3-5,EE 7 |(Ey)(Ex)Lxy 1,2-6,EE SET E PROB D 1 |(Ex)(y)Lxy / (y)(Ex)Lxy +--------------------- 2 |a|(y)Lay A | +--------------------- 3 | |Lab 2,UE 4 | |(Ex)Lxb 3,EI 5 | |(y)(Ex)Lxy 4,UI 6 |(y)(Ex)Lxy 1,2-5,EE SET E PROB E 1 |(x)Px & (x)Qx / (x)(y)(Px & Qy) +--------------------- 2 |(x)Px 1,&E 3 |(x)Qx 1,&E 4 |Pa 2,UE 5 |Qb 3,UE 6 |Pa & Qb 4,5,&I 7 |(y)(Pa & Qy) 6,UI 8 |(x)(y)(Px & Qy) 7,UI SET E PROB F 1 |(Ex)Px & (Ex)Qx / (Ex)(Ey)(Px & Qy) +--------------------- 2 |(Ex)Px 1,&E 3 |(Ex)Qx 1,&E 4 |a|Pa A | +--------------------- 5 | |(Ex)Qx 3,R 6 | |b|Qb A | | +--------------------- 7 | | |Pa 4,R 8 | | |Pa & Qb 6,7,&I 9 | | |(Ey)(Pa & Qy) 8,EI 10 | | |(Ex)(Ey)(Px & Qy) 9,EI 11 | |(Ex)(Ey)(Px & Qy) 5,6-10,EE 12 |(Ex)(Ey)(Px & Qy) 2,4-11,EE SET E PROB G 1 |(x)Px v (x)Qx / (x)(y)(Px v Qy) +--------------------- 2 | |(x)Px A | +--------------------- 3 | |Pa 2,UE 4 | |Pa v Qb 3,vI 5 | 6 | |(x)Qx A | +--------------------- 7 | |Qb 6,UE 8 | |Pa v Qb 7,vI 9 | 10 |Pa v Qb 1,2-4,6-8,AC 11 |(y)(Pa v Qy) 10,UI 12 |(x)(y)(Px v Qy) 11,UI SET E PROB H 1 |(Ex)Px v (Ex)Qx / (Ex)(Ey)(Px v Qy) +--------------------- 2 | |(Ex)Px A | +--------------------- 3 | |a|Pa A | | +--------------------- 4 | | |Pa v Qb 3,vI 5 | | |(Ey)(Pa v Qy) 4,EI 6 | | |(Ex)(Ey)(Px v Qy) 5,EI 7 | |(Ex)(Ey)(Px v Qy) 2,3-6,EE 8 | 9 | |(Ex)Qx A | +--------------------- 10 | |b|Qb A | | +--------------------- 11 | | |Pa v Qb 10,vI 12 | | |(Ey)(Pa v Qy) 11,EI 13 | | |(Ex)(Ey)(Px v Qy) 12,EI 14 | |(Ex)(Ey)(Px v Qy) 9,10-13,EE 15 | 16 |(Ex)(Ey)(Px v Qy) 1,2-7,9-14,AC SET E PROB I 1 |(Ex)(Ey)(Px v Qy) / (Ex)Px v (Ex)Qx +--------------------- 2 |a|(Ey)(Pa v Qy) A | +--------------------- 3 | |b|Pa v Qb A | | +--------------------- 4 | | | |Pa A | | | +--------------------- 5 | | | |(Ex)Px 4,EI 6 | | | |(Ex)Px v (Ex)Qx 5,vI 7 | | | 8 | | | |Qb A | | | +--------------------- 9 | | | |(Ex)Qx 8,EI 10 | | | |(Ex)Px v (Ex)Qx 9,vI 11 | | | 12 | | |(Ex)Px v (Ex)Qx 3,4-6,8-10,AC 13 | |(Ex)Px v (Ex)Qx 2,3-12,EE 14 |(Ex)Px v (Ex)Qx 1,2-13,EE SET E PROB J 1 |(x)(y)(Lxy > ~Lxy) / (x)~Lxx +--------------------- 2 | |Laa A | +--------------------- 3 | |(x)(y)(Lxy > ~Lxy) 1,R 4 | |(y)(Lay > ~Lay) 3,UE 5 | |Laa > ~Laa 4,UE 6 | |~Laa 2,5,>E 7 |~Laa 2,6,(2-6),~I 8 |(x)~Lxx 7,UI SET E PROB K 1 |(x)(y)(Px > Qy) / (Ex)Px > (x)Qx +--------------------- 2 | |(Ex)Px A | +--------------------- 3 | |a|Pa A | | +--------------------- 4 | | |(x)(y)(Px > Qy) 1,R 5 | | |(y)(Pa > Qy) 4,UE 6 | | |Pa > Qb 5,UE 7 | | |Qb 3,6,>E 8 | | |(x)Qx 7,UI 9 | |(x)Qx 2,3-8,EE 10 |(Ex)Px > (x)Qx 2-9,>I SET E PROB L Rest of set omitted