Given the relation $A \times A$, where $A = \{2, 3, 4, 5\}$, we need to find the set of all ordered pairs $(x, y)$ such that $x > 4$ and $y < 4$.

Step-by-Step Solution:

1. Identify the elements of set $A$: $A = \{2, 3, 4, 5\}$

2. Determine the condition $x > 4$:

   • Since $x$ must be greater than 4 and $x$ is an element of $A$, the only possible value for $x$ is 5.

3. Determine the condition $y < 4$:

   • Since $y$ must be less than 4 and $y$ is an element of $A$, the possible values for $y$ are 2 and 3.

4. Form the set of ordered pairs:

   • The ordered pairs $(x, y)$ satisfying the given conditions are: $(5, 2) \quad \text{and} \quad (5, 3)$

Final Answer:

The set indicated by $\{(x, y) \mid x > 4 \text{ and } y < 4\}$ is: $\{(5, 2), (5, 3)\}$

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the Cartesian product of two sets?
2. How do you determine the domain and range of a relation?
3. How would the answer change if the condition was $x \geq 4$ and $y < 4$?
4. What is the difference between a relation and a function?
5. How do you represent a relation using a matrix?

Tip: Always ensure the conditions given in a problem are applied correctly to every element in the set before forming the final answer.