Задание 2 ЕГЭ по информатике 2027: таблицы истинности

from itertools import permutations


def f(w, x, y, z):
    # F = (¬z ∧ w) ∨ (x → y); импликация ложна только при x = 1 и y = 0
    first = 1 if (z == 0 and w == 1) else 0
    second = 0 if (x == 1 and y == 0) else 1
    return first or second


# все строки таблицы истинности: значения переменных и функции
rows = []
for w in (0, 1):
    for x in (0, 1):
        for y in (0, 1):
            for z in (0, 1):
                rows.append({'w': w, 'x': x, 'y': y, 'z': z, 'F': f(w, x, y, z)})

# фрагмент из условия: None — пустая клетка, последний столбец — F
fragment = [
    [None, 0, 0, 1, 0],
    [None, 0, None, None, 0],
    [None, 0, None, 0, 0],
]


def fits(columns, order):
    # сходятся ли заполненные клетки фрагмента с выбранными строками
    for frag_row, row in zip(fragment, order):
        values = [row[c] for c in columns] + [row['F']]
        if any(v is not None and v != values[j] for j, v in enumerate(frag_row)):
            return False
    return True


for columns in permutations('wxyz'):
    if any(fits(columns, order) for order in permutations(rows, len(fragment))):
        print(''.join(columns))
        break

from itertools import permutations


def f(x, y, z):
    # F = ((x ∨ y) ≡ ¬y) ∨ (¬x ≡ (x ∨ z))
    left = ((x or y) == (1 - y))
    right = ((1 - x) == (x or z))
    return int(left) or int(right)


rows = []
for x in (0, 1):
    for y in (0, 1):
        for z in (0, 1):
            rows.append({'x': x, 'y': y, 'z': z, 'F': f(x, y, z)})

# фрагмент из условия: None — пустая клетка, последний столбец — F
fragment = [
    [None, 0, 1, 0],
    [0, 1, None, 0],
    [None, 0, None, 0],
]


def fits(columns, order):
    for frag_row, row in zip(fragment, order):
        values = [row[c] for c in columns] + [row['F']]
        if any(v is not None and v != values[j] for j, v in enumerate(frag_row)):
            return False
    return True


for columns in permutations('xyz'):
    if any(fits(columns, order) for order in permutations(rows, len(fragment))):
        print(''.join(columns))
        break

from itertools import permutations


def f(w, x, y, z):
    # F = (¬z → ¬y) → (x ∨ ¬w)
    premise = 0 if (z == 0 and y == 1) else 1   # ¬z → ¬y ложно при z = 0 и y = 1
    consequence = 1 if (x == 1 or w == 0) else 0
    # импликация ложна, только если посылка истинна, а следствие ложно
    return int((1 - premise) or consequence)


rows = []
for w in (0, 1):
    for x in (0, 1):
        for y in (0, 1):
            for z in (0, 1):
                rows.append({'w': w, 'x': x, 'y': y, 'z': z, 'F': f(w, x, y, z)})

# фрагмент из условия: None — пустая клетка, последний столбец — F
fragment = [
    [0, None, 1, None, 0],
    [0, None, 1, 0, 0],
    [1, 1, None, None, 0],
]


def fits(columns, order):
    for frag_row, row in zip(fragment, order):
        values = [row[c] for c in columns] + [row['F']]
        if any(v is not None and v != values[j] for j, v in enumerate(frag_row)):
            return False
    return True


for columns in permutations('wxyz'):
    if any(fits(columns, order) for order in permutations(rows, len(fragment))):
        print(''.join(columns))
        break

from itertools import permutations


def f(w, x, y, z):
    # F = ((y ∧ w) ∧ (¬z → ¬w)) ≡ ((y → x) → (y → z))
    left = (y == 1 and w == 1 and (z == 1 or w == 0))
    imp1 = (y == 0 or x == 1)   # y → x
    imp2 = (y == 0 or z == 1)   # y → z
    right = (not imp1) or imp2
    return int(left == right)


rows = []
for w in (0, 1):
    for x in (0, 1):
        for y in (0, 1):
            for z in (0, 1):
                rows.append({'w': w, 'x': x, 'y': y, 'z': z, 'F': f(w, x, y, z)})

# фрагмент из условия: None — пустая клетка, последний столбец — F
fragment = [
    [1, None, None, None, 1],
    [1, 1, 0, None, 1],
    [0, 1, 0, None, 1],
    [1, None, 1, 0, 1],
]


def fits(columns, order):
    for frag_row, row in zip(fragment, order):
        values = [row[c] for c in columns] + [row['F']]
        if any(v is not None and v != values[j] for j, v in enumerate(frag_row)):
            return False
    return True


for columns in permutations('wxyz'):
    if any(fits(columns, order) for order in permutations(rows, len(fragment))):
        print(''.join(columns))
        break