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
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B
1
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AB
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B
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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
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(+ )
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B
, A
B,
1
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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
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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,
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