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))