Find a bijection from X to Y without conditionals in Python

In mathematics, a bijection is a function between the two sets that is both injective and surjective. Finding a bijection from the set X to set Y without using the conditionals involves mapping each element of X to the unique element of the Y without relying on the if-else statements. In this article, we will explain the methods of Finding a bijection from X to Y without conditionals in Python.

Example :

Input : X = {1, 2, 3, 4}
            Y = {'a', 'b', 'c', 'd'}
Output: {1: 'a', 2: 'c', 3: 'b', 4: 'd'}
Explanation : Here we are two sets X ,Y then we implemented bijection on X and Y and print the result. 

Find a Bijection From X to Y without Conditionals in Python

Below, are the code examples of Find a bijection from X to Y without conditionals in Python.

Find a Bijection From X to Y Using Dictionary Comprehension

In this example, the below code defines two sets, X and Y, containing integer and character elements respectively. It then creates a bijection from X to Y using dictionary comprehension, pairing each element from X with its corresponding element from Y using the zip() function.

Python

# Define sets X and Y
X = {1, 2, 3, 4}
Y = {'a', 'b', 'c', 'd'}

# Create a bijection using dictionary comprehension
bijection = {x: y for x, y in zip(X, Y)}

print("Bijection from X to Y:")
print(bijection)

Output

Bijection from X to Y:
{1: 'a', 2: 'c', 3: 'b', 4: 'd'}

Find a Bijection From X to Y Using Enumerate Functions

In this example, below code defines sets X and Y with numeric and alphabetic elements respectively, then creates a bijection from X to Y using the intersection of X and Y along with enumerate(). It pairs each element from X with its corresponding element from Y based on their positions in the intersection.

Python

# Define sets X and Y
X = {1, 2, 3, 4}
Y = {'a', 'b', 'c', 'd'}

# Create a bijection using enumerate and set intersection
bijection = {x: Y[i] for i, x in enumerate(X & Y)}

print("Bijection from X to Y:")
print(bijection)

Output

Bijection from X to Y:
{}