1 1
2
A
1 1
2 A, B A B
A
1 1 , C , C
2 A, B A B
A
AB (B A) C
1
, A
AB
,
B
1
, A
AB
,
B
(A B ) B, (A B )
B.
1
Prove (A B ) B (B A) A.
(A B ) B, (A B )
B.
(A B ) B, (A B ) (A B ) B, (A B ) (A B ) B, (A B )
(A B ) B (A B ) B
1
Prove (A B ) B (B A)
1.
(1) (A B ) B (B A) A; (2) (A B ) C (A C ) C ; (3) (A B ) C ) (C A) (D A);1 (4) (A B ) (D C ), B A, A C A D.
2.
(1) (A B ) A B ; (2) (A B ) A B ; (3) A A. (+ ) 3.
A
( ),
(+ )
, A
B
, A
B,
1
b R YX VU S PHF DCBA98765431 2Q2P22a2`22IW2G@82T22R2Q22IGE22222
1
0,1.
TR EP GH7 F S 6 QI '!" B"BD3CB!BB EBBBB!BB @" A 9 @ 7)4)0()'&$%#"! 8 65 321
2 p, q, r; .
p1 , p2, ., pn, .
2
(c) Either Sam will come to the party and Max will
not, or Sam will not come to the party and Max will enjoy himself.
2
(c) Either Sam w
1.
2.
(a) If Mr Jones is happy, Mrs Jones is not happy,and if Mr Jones is not happy, Mrs Jones is not happy. (b) A sucient condition for x to be odd is that x is prime. (c) Either Sam will come to the party and Max will not, or Sam will not come to the pa
Notation: fij denotes the i-th j -ary function symbol, and pj the i-th j -ary i predicate symbol. 1. Pick out the free and bound occurrences of variables in the following formulas: (a) x3 (x1 p2 (x1 , x2 ) p2 (x3 , a1 ); 1 1 (b) x2 p2 (x3 , x2 ) x3 p2 (x3
qS sr A AAAAt AC T P I x w v Y AdyAAAAAAuHt `$ #W H V " @! sr q T C Y S19P4I G F )gWV ( 9a c i ) a gWV 0 ' & p G F ) gWV ' & h 5 A)f e a AAC Y 0X ca dbH ` GF A8 ED UC YU8 X ( UUUUUUUVUUUTU1RQI @! $#W CB S P
A =1
v
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1 2 A cfw_A : (A)v = 1 = . 3. 4. 2. (6) (5) 1 2 1 1 2 2 v v (p) = 1 A 1 v, , A 2 . 1 p ; cfw_A : (A)v = 1 1 2 , 1 2 , v 2 , p,
D B C A @ 7 8 $ # & "