Solves Part D and F from https://math.stackexchange.com/q/1835846/307483

test_all_possibilities.py

def implies(x, y):
    '''Tells us if x --> y'''
    return ((not x) or y)

def digits(num, base=10):
    '''Converts num to an array containing its digits from base specified'''
    if num < base: return [num]
    return digits((num-(num % base))//base, base)+[num % base]

# Answer for part d
d = 0
# Answer for part f
f = 0
# Print notice so people can understand messages:
print("Correct answers will be printed in the form [a, b, c, d, e, f, g, h]")
print("0 represents false, 1 represents true")
# Loop through 256 possibilities
for i in range(256):
    # Convert possibilities to binary and add leading 0s to get Booleans
    bits = digits(i, 2)
    while len(bits) < 8: bits = [0]+bits

    # Incremend d if applicable
    if implies(bits[0], bits[1]) and implies(bits[1], bits[0]) and implies(bits[2], bits[3]) and implies(bits[3], bits[4]) and implies(bits[4], bits[5]) and implies(bits[5], bits[6]) and implies(bits[6], bits[7]):
        d += 1
        # Print the applicable bits
        print("D is true when we have", bits)

    # Increment f if applicable
    if implies(bits[7], bits[0]) and implies(bits[0], (bits[1] and bits[2])) and implies((bits[1] or bits[2]), bits[3]) and implies(bits[0], bits[4]) and implies(bits[4], bits[5]) and implies(bits[5], bits[6]) and implies(bits[6], bits[7]):
        f += 1
        # Print the applicable bits
        print("F is true when we have", bits)

# Print answers
print(d, f)