List the elements of the given set. Although the elements in a set can be listed in any order, type your answer in order from smallest to largest using commas between elements.

[tex]\[ \{x \mid x \in N \text{ and } 12 \ \textless \ x \leq 17\} \][/tex]



Answer :

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]