213 lines
3.3 KiB
Markdown
Executable File
213 lines
3.3 KiB
Markdown
Executable File
# Рабочая тетрадь № 5
|
||
|
||
## Задачи № 1
|
||
|
||
### № 1
|
||
|
||
```math
|
||
¬( ( x ∧ y ) ∨ ̅z ) ≡ ¬( z → x ) ∨ ¬( z → y )
|
||
¬( x ∧ y ) ∧ z ≡ ¬( ̅z ∨ x ) ∨ ¬( ̅z ∨ y )
|
||
( ̅x ∨ ̅y ) ∧ z ≡ ( z ∧ ̅x ) ∨ ( z ∧ ̅y )
|
||
( ̅x ∨ ̅y ) ∧ z ≡ z ∧ ( ̅x ∨ ̅y )
|
||
( ̅x ∨ ̅y ) ∧ z ≡ ( ̅x ∨ ̅y ) ∧ z
|
||
```
|
||
|
||
### № 2
|
||
|
||
```math
|
||
¬( ( x ∧ y ) ∨ ̅z) ≡ ¬( z → x ) ∨ ¬( z → y )
|
||
|
||
x y z f1 f2
|
||
0 0 0 0 0
|
||
0 0 1 1 1
|
||
0 1 1 1 1
|
||
0 1 0 0 0
|
||
1 0 0 0 0
|
||
1 0 1 1 1
|
||
1 1 0 0 0
|
||
1 1 1 0 0
|
||
```
|
||
|
||
### № 3
|
||
|
||
```math
|
||
F(x,y,z) = ( ̅z → x ) ↔ ( ̅x │ y )
|
||
|
||
x y z f
|
||
0 0 0 0
|
||
0 0 1 1
|
||
0 1 1 0
|
||
0 1 0 1
|
||
1 0 0 1
|
||
1 0 1 1
|
||
1 1 0 1
|
||
1 1 1 1
|
||
|
||
ДНФ: ( y ∧ ̅z ) ∨ ( ̅y ∧ z ) ∨ x
|
||
КНФ: ( x ∨ ̅y ∨ z ) ∧ ( x ∨ y ∨ z )
|
||
```
|
||
|
||
### № 4
|
||
|
||
```math
|
||
A = ( x → y ) ∧ ( x → ̅y ) ∧ x
|
||
A = ( ̅x ∨ y ) ∧ ( ̅x ∨ ̅y ) ∧ x
|
||
A = ( ̅x ∨ ( y ∧ ̅y ) ) ∧ x
|
||
A = ( ̅x ∨ 0 ) ∧ x
|
||
A = ̅x ∧ x
|
||
A = 0
|
||
```
|
||
|
||
## Задачи № 2
|
||
|
||
### № 1
|
||
|
||
```math
|
||
1) x ∧ y ∨ x ∧ y ∨ ̅x ∧ ̅y
|
||
( x ∧ y ) ∨ ( ̅x ∧ ̅y )
|
||
( x ∧ y ) ∨ ( ̅x ∧ ̅y )
|
||
x ↔ y
|
||
2) ( x ∨ ̅y ) ∧ ( ̅x ∨ y ) ∧ ( ̅x ∨ ̅y )
|
||
( x ∨ ̅y ) ∧ ̅x
|
||
( x ∧ ̅x ) ∨ ( ̅y ∧ ̅x )
|
||
0 ∨ ¬( y ∧ x )
|
||
y | x
|
||
```
|
||
|
||
### № 2
|
||
|
||
```math
|
||
( x1 ∨ x2 ∨ x3 ) ∧ ( ̅x1 ∨ ̅x2 ∨ x3 ) ∧ ( x1 ∨ x2 ∨ ̅x3 ) ∧ ( ̅x1 ∨ ̅x2 ∨ ̅x3 )
|
||
```
|
||
|
||
### № 3
|
||
|
||
```math
|
||
1) ( x ∨ ̅x )
|
||
2) ( ̅x ∧ ̅y ) ∨ ( x ∧ y ) ∨ ( ̅x ∧ y ) ∨ ( x ∧ ̅y )
|
||
```
|
||
|
||
### № 4
|
||
|
||
```math
|
||
1) ( x ∧ ̅x )
|
||
2) ( ̅x ∨ ̅y ) ∧ ( x ∨ y ) ∧ ( ̅x ∨ y ) ∧ ( x ∨ ̅y )
|
||
```
|
||
|
||
### № 5
|
||
|
||
```math
|
||
CДНФ: ( x ∧ y ∧ z ) ∨ ( ̅x ∧ y ∧ z ) ∨ ( ̅x ∧ ̅y ∧ z )
|
||
CКНФ: ( x ∨ y ∨ z ) ∧ ( x ∨ ̅y ∨ z ) ∧ ( ̅x ∨ y ∨ z ) ∧ ( ̅x ∨ y ∨ ̅z ) ∧ ( ̅x ∨ ̅y ∨ z )
|
||
```
|
||
|
||
## Тест № 5
|
||
|
||
1. 4
|
||
2. 1
|
||
3. 1
|
||
4. 2
|
||
5. 1
|
||
6. 3
|
||
7. 4
|
||
8. 2
|
||
9. 2
|
||
10. 4
|
||
|
||
## Задачи № 3
|
||
|
||
### № 1
|
||
|
||
```python
|
||
a = int(input())
|
||
if 100 <= a < 1000 and a % 5 == 0:
|
||
print("Является")
|
||
else:
|
||
print("Не является")
|
||
```
|
||
|
||
### № 2
|
||
|
||
```python
|
||
a = int(input())
|
||
b = int(input())
|
||
c = int(input())
|
||
|
||
if (a % 2) + (b % 2) + (c % 2) <= 1:
|
||
print("2 и более")
|
||
else:
|
||
print("Меньше 2")
|
||
|
||
```
|
||
|
||
### № 3
|
||
|
||
```python
|
||
x, y = float(input()), float(input())
|
||
|
||
if (x >= 0 and x**2 + y**2 <= 1) or (y <= 1 and x >= 0 and y >= x - 1):
|
||
print("Yes")
|
||
else:
|
||
print("No")
|
||
|
||
```
|
||
|
||
### № 4
|
||
|
||
```python
|
||
import math as m
|
||
|
||
|
||
x, y = float(input()), float(input())
|
||
|
||
if (y <= m.sin(x) and 0 <= y <= 0.5 and 0 <= x <= m.pi):
|
||
print("Yes")
|
||
else:
|
||
print("No")
|
||
```
|
||
|
||
### № 5
|
||
|
||
```python
|
||
x, y = float(input()), float(input())
|
||
if (x <= 0 and x**2 + y**2 <= 1) or (x**2 + y**2 <= 1 and y >= x):
|
||
print("Yes")
|
||
else:
|
||
print("No")
|
||
|
||
```
|
||
|
||
## Задачи № 4
|
||
|
||
### № 1
|
||
|
||
```python
|
||
# 3
|
||
x, y = float(input()), float(input())
|
||
|
||
if (x >= 0 and x**2 + y**2 <= 1) or (y <= 1 and x >= 0 and y >=// x - 1):
|
||
print("Yes")
|
||
else:
|
||
print("No")
|
||
|
||
# 4
|
||
import math as m
|
||
|
||
|
||
x, y = float(input()), float(input())
|
||
|
||
if (y <= m.sin(x) and 0 <= y <= 0.5 and 0 <= x <= m.pi):
|
||
print("Yes")
|
||
else:
|
||
print("No")
|
||
|
||
# 5
|
||
x, y = float(input()), float(input())
|
||
|
||
if (x <= 0 and x**2 + y**2 <= 1) or (x**2 + y**2 <= 1 and y >= x):
|
||
print("Yes")
|
||
else:
|
||
print("No")
|
||
|
||
```
|