Selected Answers from 8.1

8.1 ex I

1.	Premise 1 (^x)Ax 1 ^E 2 Aa 1 ^E 3 Ab 2,3 &I 4 Aa&Ab
3.	Assumption 1 ....what if (^x)(Tx&~Ux) 1 ^E 2 ....then... Ta&~Ua 2 &E 3 ....then... Ta 3 %I 4 ....then... (%y)Ty 1-4 >I 5 (^x)(Tx&~Ux)>(%y)Ty
5.	Premise 1 (^y)(Ty>Uy) Premise 2 Ta 1 ^E 3 Ta>Ua 2,3 >E 4 Ua 2,4 &I 5 Ua&Ta 5 %I 6 (%z)(Uz&Tz)

8.1 ex II

1.	Premise 1 (^x)(AxvBx) 1 CM 2 (^x)(Bx v Ax)
3.	Assumption 1 ....what if Ta 1 R 2 ....then... Ta 1-2 >I 3 Ta>Ta   3 IM 4 ~Ta v Ta   4 CM 5 Ta v ~Ta   5 %I 6 (%x)(Tx v ~Tx)
5.	Premise 1 (^y)((TyvKy)>Uy) Premise 2 Ka 1 ^E 3 (Ta v Ka)>Ua 2 vI 4 Ta v Ka 3,4 >E 5 Ua 5 %I 6 (%z)Uz