





import math



def 	_a						(   UpperCAmelCase					)    ->    bool:







   """simple docstring"""

   if 1 < number < 4:
      # 2 and 3 are primes
      return True
   elif number < 2 or number % 2 == 0 or number % 3 == 0:
      # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
      return False

   # All primes number are in format of 6k +/- 1
   for i in range(5      ,  int(math.sqrt(UpperCAmelCase					) + 1					)      ,  6					):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True



def 	_a						(   UpperCAmelCase = 10001					)    ->    int:







   """simple docstring"""

   try:
      lowerCamelCase__       :						Tuple        =							int(UpperCAmelCase					)
   except (TypeError, ValueError):
      raise TypeError('''Parameter nth must be int or castable to int.'''					) from None
   if nth <= 0:
      raise ValueError('''Parameter nth must be greater than or equal to one.'''					)
   lowerCamelCase__       :						list[int]        =							[]
   lowerCamelCase__       :						str        =							2
   while len(UpperCAmelCase					) < nth:
      if is_prime(UpperCAmelCase					):
         primes.append(UpperCAmelCase					)
         num += 1
      else:
         num += 1
   return primes[len(UpperCAmelCase					) - 1]


if __name__ == "__main__":
       print(F'''{solution() = }''')













import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
       # Create universe of discourse in Python using linspace ()
       _A :   Optional[int]  			=  np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False)

       # Create two fuzzy sets by defining any membership function
       # (trapmf(), gbellmf(), gaussmf(), etc).
       _A :   Any  			=  [0, 25, 50]
       _A :   Dict  			=  [25, 50, 75]
       _A :   Any  			=  fuzz.membership.trimf(X, abca)
       _A :   List[Any]  			=  fuzz.membership.trimf(X, abca)

       # Compute the different operations using inbuilt functions.
       _A :   List[str]  			=  np.ones(75)
       _A :   Optional[int]  			=  np.zeros((75,))
       # 1. Union = max(µA(x), µB(x))
       _A :   Optional[Any]  			=  fuzz.fuzzy_or(X, young, X, middle_aged)[1]
       # 2. Intersection = min(µA(x), µB(x))
       _A :   Union[str, Any]  			=  fuzz.fuzzy_and(X, young, X, middle_aged)[1]
       # 3. Complement (A) = (1- min(µA(x))
       _A :   List[Any]  			=  fuzz.fuzzy_not(young)
       # 4. Difference (A/B) = min(µA(x),(1- µB(x)))
       _A :   Tuple  			=  fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
       # 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
       _A :   List[Any]  			=  young + middle_aged - (young * middle_aged)
       # 6. Algebraic Product = (µA(x) * µB(x))
       _A :   Optional[Any]  			=  young * middle_aged
       # 7. Bounded Sum = min[1,(µA(x), µB(x))]
       _A :   Dict  			=  fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
       # 8. Bounded difference = min[0,(µA(x), µB(x))]
       _A :   List[str]  			=  fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

       # max-min composition
       # max-product composition

       # Plot each set A, set B and each operation result using plot() and subplot().
       from matplotlib import pyplot as plt

       plt.figure()

       plt.subplot(4, 3, 1)
       plt.plot(X, young)
       plt.title('Young')
       plt.grid(True)

       plt.subplot(4, 3, 2)
       plt.plot(X, middle_aged)
       plt.title('Middle aged')
       plt.grid(True)

       plt.subplot(4, 3, 3)
       plt.plot(X, union)
       plt.title('union')
       plt.grid(True)

       plt.subplot(4, 3, 4)
       plt.plot(X, intersection)
       plt.title('intersection')
       plt.grid(True)

       plt.subplot(4, 3, 5)
       plt.plot(X, complement_a)
       plt.title('complement_a')
       plt.grid(True)

       plt.subplot(4, 3, 6)
       plt.plot(X, difference)
       plt.title('difference a/b')
       plt.grid(True)

       plt.subplot(4, 3, 7)
       plt.plot(X, alg_sum)
       plt.title('alg_sum')
       plt.grid(True)

       plt.subplot(4, 3, 8)
       plt.plot(X, alg_product)
       plt.title('alg_product')
       plt.grid(True)

       plt.subplot(4, 3, 9)
       plt.plot(X, bdd_sum)
       plt.title('bdd_sum')
       plt.grid(True)

       plt.subplot(4, 3, 10)
       plt.plot(X, bdd_difference)
       plt.title('bdd_difference')
       plt.grid(True)

       plt.subplots_adjust(hspace=0.5)
       plt.show()



