To solve the given problem, we need to list the elements of the set defined by the condition [tex]\( \{x \mid x \in \mathbb{N} \text{ and } 12 < x \leq 17\} \)[/tex].
1. Firstly, identify the range of values [tex]\( x \)[/tex] can take based on the given condition.
2. The condition states that [tex]\( x \)[/tex] must be a natural number ([tex]\( x \in \mathbb{N} \)[/tex]).
3. Additionally, [tex]\( x \)[/tex] must satisfy [tex]\( 12 < x \leq 17 \)[/tex].
Let’s find all the natural numbers that satisfy [tex]\( 12 < x \leq 17 \)[/tex]:
- [tex]\( x > 12 \)[/tex], so the smallest possible value for [tex]\( x \)[/tex] is 13.
- [tex]\( x \leq 17 \)[/tex], so the largest possible value for [tex]\( x \)[/tex] is 17.
Now, we list all the natural numbers between 12 and 17 (not including 12 but including 17):
13, 14, 15, 16, 17
Therefore, the elements of the set [tex]\( \{x \mid x \in \mathbb{N} \text{ and } 12 < x \leq 17\} \)[/tex] listed in order from smallest to largest are:
[tex]\[ 13, 14, 15, 16, 17 \][/tex]
