$$ \text{Given that }E\text{ \textbraceleft}4<x\le\text{ }13\rbrace\text{ list the elements of the following sets( }A=\left\lbrace x:\text{  }x\text{ is odd}\right\rbrace\text{. }B=\text{ \textbraceleft}x\text{ :  }x\text{ is a prime number\textbraceright} $$

Given the set $ E = \{ x \mid 4 < x \leq 13 \} $, we are asked to list the elements of two sets:

1. $ A = \{ x \mid x \text{ is odd} \} $
2. $ B = \{ x \mid x \text{ is a prime number} \} $

### Step 1: Identify the elements of $ E $
The set $ E = \{ x \mid 4 < x \leq 13 \} $ includes all integers greater than 4 and less than or equal to 13. So, 
\[ E = \{ 5, 6, 7, 8, 9, 10, 11, 12, 13 \} \]

### Step 2: List the elements of set $ A $ (Odd numbers)
We need to find the odd numbers in the set $ E $:
\[ A = \{ 5, 7, 9, 11, 13 \} \]

### Step 3: List the elements of set $ B $ (Prime numbers)
We need to find the prime numbers in the set $ E $:
- 5 is prime.
- 7 is prime.
- 11 is prime.
- 13 is prime.
- 6, 8, 9, 10, and 12 are not prime.

So, 
\[ B = \{ 5, 7, 11, 13 \} \]

### Summary
- The elements of set $ A $ are: $ \{ 5, 7, 9, 11, 13 \} $
- The elements of set $ B $ are: $ \{ 5, 7, 11, 13 \} $

Would you like further details or explanations on this problem?

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Here are 5 related questions for further practice:
1. What is the intersection of sets $ A $ and $ B $?
2. Find the union of sets $ A $ and $ B $.
3. Determine the complement of set $ A $ within set $ E $.
4. List the elements of $ E $ that are even.
5. What is the difference between sets $ A $ and $ B $?

**Tip:** When identifying prime numbers, remember that a prime number has exactly two distinct positive divisors: 1 and the number itself.

Explore how to list elements of sets A (odd numbers) and B (prime numbers) within a specified range using set theory and number theory. Suitable for Grades 6-8 students learning about sets, odd numbers, and prime numbers.

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