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The question is asking to determine the correct Cartesian product between the sets \( E = \{0, 1, 2\} \) and \( F = \{4, 5\} \).

The Cartesian product \( E \times F \) is defined as the set of all ordered pairs \( (e, f) \), where \( e \in E \) and \( f \in F \). So, we need to calculate:

\[
E \times F = \{ (e, f) \mid e \in E, f \in F \}
\]

Given \( E = \{0, 1, 2\} \) and \( F = \{4, 5\} \), we compute the pairs:

- When \( e = 0 \): \( (0, 4), (0, 5) \)
- When \( e = 1 \): \( (1, 4), (1, 5) \)
- When \( e = 2 \): \( (2, 4), (2, 5) \)

So, the Cartesian product \( E \times F \) is:

\[
\{(0, 4), (0, 5), (1, 4), (1, 5), (2, 4), (2, 5)\}
\]

Now, looking at the options:

- **A**: This contains pairs such as \( (4, 0) \), \( (4, 1) \), which are not part of the Cartesian product.
- **B**: This set includes \( (0, 4), (0, 5), (1, 4), (1, 5), (2, 4) \) but is missing \( (2, 5) \).
- **C**: This set has pairs \( (4, 5) \) and \( (5, 0) \), which are incorrect.
- **D**: This contains the correct set of ordered pairs: \( \{(0, 4), (0, 5), (1, 4), (1, 5), (2, 4), (2, 5)\} \).
- **E**: This set contains pairs \( (0, 5), (0, 1), (1, 4) \), which are incorrect.

Thus, the correct answer is **D**.

Would you like further details on Cartesian products? Here are some related questions for you to explore:

1. What is the definition of a Cartesian product in set theory?
2. How do you calculate the Cartesian product of more than two sets?
3. What are some applications of Cartesian products in mathematics and computer science?
4. How is the concept of ordered pairs important in the Cartesian product?
5. Can the Cartesian product be applied to infinite sets, and how?

**Tip:** When calculating a Cartesian product, remember that order matters in the pair \( (e, f) \), where \( e \) comes from the first set, and \( f \) comes from the second set.

Considere os seguintes conjuntos: E = {0, 1, 2}; e F = {4, 5}. É correto afirmar que o produto cartesiano formado entre eles (E × F) é dado por:

Learn how to calculate the Cartesian product between sets E = {0, 1, 2} and F = {4, 5}. The Cartesian product includes all ordered pairs (e, f) where e is from set E and f is from set F. This is a key concept in set theory suitable for high school students.

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