a0a2a1a4a3a4a5a4a6a8a7a10a9a12a11a12a13a12a14a12a15a12a16a12a14a12a17
1. (a18a20a19 2 a21a20a22a2a23 10 a21 ) a24a20a25a20a19a27a26a29a28a20a30a20a31a20a22a2a32a20a33a20a19a20a34a20a35a20a36a20a37a39a38a41a40
pa42a2a43
a32a20a22a2a40
a44a46a45
(a) ( )a28a48a47a48a49a48a50a48a49 A a51a48a52a48a53a48a49a48a54a48a55a48a56a48a54a48a47a48a49a48a50a48a49 B a51a48a52a48a53a48a49a48a22a57a32 A B
a51a20a52a20a53a20a49a20a58
(b) ( ) a28a20a47a20a49a20a50a20a49 A a51a20a59a20a60a20a61a20a35a20a22a62a32 A a51a20a63a20a59a20a60a20a61a20a35a20a58
(c) ( )8x(P(x;x) 8y P(x;y)) a51a20a59a20a60a20a61a20a35a20a58
(d) ( ) a64 P0 a51a20a65a20a66a39a67 P a68a20a69a20a70a20a71a20a72a20a66a20a47a20a49a20a50a20a49 p q a73a20a74a20a50a20a75a20a76a20a77a20a78
a35a20a68a20a69a20a22a62a32 P0 a51a20a79a20a80a20a35a20a58
(e) ( ) a81a83a82a83a84a83a66a83a85a83a86a83a87a83a88a83a22a62a65a83a89a83a90a83a91a83a92a83a49a83a68a83a69 F1
a93
F2 a35a83a94a83a95a83a96a83a37a83a97
a98
a58a62a28 F1 F2 a22a62a32 Th(F1) Th(F2) TL(F1) a58
2. (a18a20a19 6 a21a20a22a62a23 18 a21 ) a99a20a100a20a19a20a45
(a) a101a20a102a39a103 P a35a20a104a20a75a20a105a20a32 MP a51a20a106a20a107a20a35a20a58
(b) a101a20a108a20a109a20a110a20a111a20a50a20a49a20a35a20a112a20a30a20a113a20a49
a93
a34a20a114a20a113a20a49a20a58
8x(x < u) (9v8w(x + v < x + w) 8z(z v < z w))
(c) a101a20a115a20a109
8x(P(x) ^Q(y) 9y( S(y;z)^R(x)))
a38a41a35a117a116a41a67a41a118a20a87a20a119a20a120a20a114a20a118a20a87a20a22a62a121a20a122a39a103a124a123a20a125a83a126a20a35a83a127 t a128a20a129a20a130a117a116a41a67a41a118a20a87a20a51a117a116
a67a41a35a20a58
3. (a18a20a19 8 a21a20a22a131a23a20a132 32 a21 ) a133a20a33 F= a68a20a69a39a38a41a108a20a109a20a110a20a111a20a82a20a75a20a35a20a102a39a103a41a134a20a135a20a58 (a136a20a137
a138a20a139 F=
a35a20a50a20a75a20a140a62a104a20a75a20a105a20a32a20a140a62a101a20a141a20a108a20a109a20a35a20a142a20a109a20a105a20a32
a93
a82a20a75 )
(a) ‘ (A B) A (a143a20a45a62a144a20a145a20a19a20a63a20a146a20a147
a138a20a139 [P]
a105a20a32 )
(b) a28 ;P(x) ‘ Q(x) a22a62a32 ;8xP(x) ‘9xQ(x) a58
(c) 8x(P(x) x = b) ‘ P(b)^8x8y(P(x) ^P(y) x = y)
(d) ‘9x(P(x) 8xP(x))
4. (10 a21 ) a64 1
a93
2 a51a20a65a20a89a20a90a20a91a20a47a20a49a20a50a20a49a20a148a20a22a149a55 1 a119 2 a63a20a79a20a80a20a58a149a101a20a102a39a103a41a45
a150a20a151
a65a20a66a20a47a20a49a20a50a20a49 A a138 a77 1 ‘ A a55 2 ‘ A a58
5. (10 a21 ) a33 F a68a20a69a39a38a41a102a39a103a41a45a62a28a20a66a20a85a20a118a20a87 y a33a20a47a20a49a20a50a20a49 A a38a41a152
a151
a109a20a153a20a22a62a32
SyxSxyA = A
6. (10 a21 ) a108a20a82a20a47a20a49a20a50a20a49 A a45
8x( R(x;x)) ^8x8y8z(R(x;y) ^R(y;z) R(x;z))^8x9yR(x;y)
a94a39a38a41a22 R a51a20a154a20a87a20a155a20a156a20a86a20a87a20a58a157a101a20a102a39a103 A a35a20a158a20a159a20a160a20a161a20a35a20a162a20a163a20a63a20a164a20a51a20a72a20a87a20a165a20a148
a42
a128a20a158a20a159a117a116a167a166a20a168 n 2 a22a62a108a20a109a20a65a20a66a20a162a20a163a39a38
a151 n
a66a20a87a20a165a20a55a20a60a20a61 A a35a20a169a20a170a20a58
7. (10a21 )a101a48a108a48a109a48a65a48a89a48a90a48a91a48a68a48a69 (a171a48a172a48a156 )F= a35a48a65a48a66a48a47a48a49a48a50a48a49a48a148 a22
a138
a77a48a128 F=
a35a20a169a20a170 < D;I0 > a51 a35a20a172a20a156a20a160a20a161a20a54a20a55a20a56a20a54 Da51a20a173a20a174a20a148a20a47a20a22a124a121a20a102a39a103a41a175a20a35a20a176
a162a20a58
1
a177a149a178a149a179a149a180 (
a181a149a182a149a183 ) a184a149a185a149a186a149a187 F= a188a149a189a149a190a149a191a149a192a149a193a149a194
(2) A 2 ‘ A
(2+) ‘ B ; A ‘ B
(2 ) ; A ‘ B ; A ‘ B ‘ B
(_+) ‘ A ‘ A _ B ; ‘ A ‘ B _ A
(_ ) ; A ‘ C ; B ‘ C ‘ A _ B ‘ C
(^+) ‘ A ‘ B ‘ A ^ B
(^ ) ‘ A ^ B ‘ A ; ‘ A ^ B ‘ B
( +) ; A ‘ B ‘ A B
( ) ‘ A ‘ A B ‘ B
( :) ‘ A B ‘ B A
(:+) ; A ‘ B ; A ‘ B ‘ A
(: ) ‘ A ‘ A ‘ B
(::+) ‘ A ‘ A
(:: ) ‘ A ‘ A
( +) ‘ A B ‘ B A ‘ A B
( ) ‘ A B ‘ A B ; ‘ A B ‘ B A
( :) ‘ A B ‘ A B
(8+) ‘ A ‘ 8xA (x a195 a196a149a197a62a198a149a199
a189a149a200 )
(8 ) ‘ 8xA ‘ Sx
t A
(t a201 A a196 x a202a62a198a149a199a204a203 )
(9+) ‘ S
x
t A
‘ 9xA (t a201 A a196 x a202a62a198a149a199a204a203 )
(9 ) ; A ‘ B ;9xA ‘ B (x a195 [fBga196a149a205a62a198a149a199 )
(C) ‘ 9xA ; S
x
y A ‘ B
‘ B
y a201 A a196a149a203 x a202a62a198a149a199a204a203a149a206
y a195 [f9xA; Bga196a149a205a62a198a149a199
(EA) ‘ x = x (x a207a149a208a149a209a149a210a149a211 )
(EAS) ‘ x = y (SzxA SzyA) (x, y a201 A a196a149a203 z a202a62a198a149a199a204a203 )
( )
‘ A
‘ A8xC8ySxyC
; ‘ A ‘ A9xC
9ySxyC
(y a195 C a196a149a205a62a198a149a199a204a206 y a201 C a196a149a203 x a202a62a198a149a199a204a203 )
([P]) a212 ‘ A1; ; ‘ An; a206 A1 ^ ^ An Ba207 P- a213a149a214a149a203 ; a191 ‘ B
([ sub1]) a212 ‘ A; M a195 A a196a149a207a149a215
a193
a203a149a206 ‘ M N; a191 ‘ AMN :
([ sub2]) a212 ‘ A; M a195 A a196a149a207a149a216
a193
a203a149a206 ‘ N M; a191 ‘ AMN :
([ sub]) a212 ‘ A; a206 ‘ M N; a191 ‘ AMN :
([sub x]) a212 ‘ A a217 x a195 a196a149a205a62a198a149a199a204a206 t a201 A a196a149a203 x a207a62a198a149a199a204a203
a191 ‘ Sx
t A:
([sub p]) a212 ‘ A a217 p a195 a196a149a205 a189a149a200 a206 D a201 A a196a149a203 p a207a62a198a149a199a204a203 a191 ‘ SpDA:
2
