consider the relation A x A where A = {2,3,4,5}.  Find the set indicated by {(x,y)|x>4 and y<4}

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.

Explore the concept of Cartesian products in set theory with a detailed solution. This problem involves finding ordered pairs (x, y) from the set A = {2, 3, 4, 5} where x > 4 and y < 4. Suitable for students in Grades 7-9.

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