2.1
| , | , | , | ||
| 1. | ||||
| 1.1 | ||||
| 2. | ||||
| 2.1 | ( 1,2,3,4,5,6,7,8) | |||
| 2.2 | ( 9) | |||
| 2.3 | ( 10) | |||
| 3. | ||||
| 3.1 . | ( 11,12,13) |
1. , .
2. . .
3. , p, q, r.
4. , p, q, r.
5. 
, , , 2 2, 1.
6. .
7. ,
) ;
)
.
8. , , , . .
9. l (x,y) D={a,b}
| x | y | l(x,y) |
| a | a | |
| a | b | |
| b | a | |
| b | b |
:
10. P(x), R(x), Q(x), S(x,y) x , x , x , y x .
:
11. 1.
1
1. 
A
A 
2. ?
3. , , q r :
: .
q: .
r: .
4. q /\, , q r :
: .
q: .
r: .
5.
|
| 3 2 |
6. (x 
|
|
|
7. x 
8. (x 
9. ∀ yl(b,y)
10. P(7)
2
1. A 
2. 1
3. ., , q r :
: .
q: .
r: .
4. ~ V ~q, , q r :
: .
q: .
r: .
5.
|
|
| 3 2 |
6. (x 
7. x∣(y 
8. 
9. ∃yl(b,y)
10. ∀x(S(2,x) ⊃R(x))
3
1. A 
2. = 3, 2 = 6.
3. , , , q r :
: .
q: .
r: .
4. ( V r) /\q, , q r :
: .
q: .
r: .
| 1 2 |
|
|
| 3 2 |
| 4 3 |
6. (x 
7. x ⋀(y ⊕ z) (x ⋀ y) ⊕ (x ⋀ z).
8. (
9. ∀x∀ yl(x,y)
10. ∃x(R(x)⋀P(x))⋀ך∃x((R(x)⋀ P(x))⋀∃y(x≠y)⋀R(y) ⋀P(y)))
4
1. A 
A 
2. !
3. , , q r :
: .
q: .
r: .
4. /\ q /\r, , q r :
: .
q: .
r: .
5.
| 1 2 |
|
|
| 3 2 |
| 4 3 |
6. (x 
7. x ⋀(y ⊕ z) (x ⋀ y) ⊕ (x ⋀ z).
8. (
9. ∀x∃yl(x,y)
10. ∀x(ךR(x) ⊃ךS(2, x))
5
1. 
2. .
3. , , , , q r :
: .
q: .
r: .
4. /\ q /\ ~r, , q r :
: .
q: .
r: .
| 1 2 |
| 3 2 |
|
|
| 4 3 |
6. (x 
7. x ⋀(y 
z) (x ⋀ y) (x ⋀ z).
8. 
9. ∃y∀xl(x,y)
10. P(7)
6
1. (
2. 2.
3. , , q r :
: .
q: .
r: .
4. /\ (~q V ~r), , q r :
: .
q: .
r: .
|
|
|
5.
| 3 2 |
|
|
| 4 3 |
6. (x 
7. x ⋀(y 
z) (x ⋀ y) (x ⋀ z).
8. 
9. ∀y ∃xl(x,y)
10. ∀x(R(x)⋀∀y(S(x,y)⊃P(y)))
7
1. 
A 
(A 
2. .
3. , , q r :
: .
q: .
r: .
4. ( V ~q) /\r, , q r :
: .
q: .
r: .
| 1 2 |
|
|
| 3 2 |
| 4 3 |
6. ( 
x
7. x ⋀(y ∣z) (x ⋀ y) ∣ (x ⋀ z).
8. 
9. ∀y∀xl(x,y)
10. ∀x(P(x)⊃∃y(R(y) ⋀S(x,y)))
8
1. 
C 
2. .
3. , , , q r :
: .
q: .
r: .
4. ( /\ r) V (q/\ ~r), , q r :
: .
q: .
r: .
| 1 2 |
|
|
| 3 2 |
| 4 3 |
6. (x 
7. x ⋁(y z) (x ⋁ y) (x ⋁z).
8. 
9. ∃x ∃yl(x,y)
10. ∀x(Q(x)⊃∀y(P(y)⊃ ךS(x,y)))
9
1. A 
(A 
2. .
3. 
, , q r :
: .
q: .
r: .
4. ( V r) /\q, , q r :
: .
q: .
r: .
5.
|
|
| 1 2 |
| 3 2 |
| 4 3 |
6. 
7. x ⋁(y ∣z) (x ⋁ y) ∣(x ⋁z).
8. (
9. ∃x∀yl(x,y)
10. R(2)⋀ P(2)
10
1. A 
(A 
2. - .
3. , q r :
: .
q: .
r: .
4. /\ q /\r, , q r :
: .
q: .
r: .
5.
|
|
| 1 2 |
| 3 2 |
| 4 3 |
6. 
7. x ⋁(y z) (x ⋁ y) (x ⋁z).
8. 
9. ∃y∃xl(x,y)
10. ∃x(R(x)⋀S(x,6))
