The image shows a diagram representing a mapping between two sets $A$ and $B$, where:

• $A = \{1, 2, 3, 4, 5\}$
• $B = \{1, 2, 3, 4\}$

The green arrows indicate the mapping from elements of $A$ to elements of $B$. Specifically:

• 1 in $A$ maps to 1 in $B$
• 2 in $A$ maps to 2 in $B$
• 3 in $A$ maps to 3 in $B$
• 4 in $A$ maps to 4 in $B$
• 5 in $A$ also maps to 4 in $B$

You are given several options:

1. Relación (Relation)
2. Función (Function)
3. Función Inyectiva (Injective Function)
4. Función Sobreyectiva (Surjective Function)
5. Función Biyectiva (Bijective Function)

Explanation:

1. Function: A function is a relation where each element in the domain (set $A$) maps to exactly one element in the codomain (set $B$). In this diagram, every element in $A$ is mapped to exactly one element in $B$, so it represents a function.

2. Injective Function: A function is injective (one-to-one) if different elements in the domain map to different elements in the codomain. Here, 4 and 5 in $A$ both map to 4 in $B$, which violates the injective condition. So, it is not injective.

3. Surjective Function: A function is surjective (onto) if every element in the codomain is mapped by at least one element in the domain. In this case, every element in $B$ is covered, so the function is surjective.

4. Bijective Function: A function is bijective if it is both injective and surjective. Since this function is not injective, it cannot be bijective.

Conclusion:

The correct answer is Función Sobreyectiva (Surjective Function).

Would you like any further details or have any questions?

Here are some related questions:

1. What is the definition of a relation in mathematics?
2. How do you determine if a function is injective?
3. What properties distinguish a surjective function from an injective function?
4. Can a function be surjective but not injective? Why or why not?
5. What is the significance of a bijective function in mathematics?

Tip: To easily check if a function is injective, look for any repeated values in the codomain. If any element in the codomain has more than one pre-image, the function is not injective.