Question
List the elements of the set, y={n|n€Z;-3 is less than or equal to 9 and 1is less than n is less than 12}
Answers
GPT-4o mini
To determine the elements of the set \( y = \{ n \mid n \in \mathbb{Z}, -3 \leq 9 \text{ and } 1 < n < 12 \} \), let's break down the conditions given:
1. The statement \( -3 \leq 9 \) is always true but does not affect the set definition.
2. We focus on the inequality \( 1 < n < 12 \), which defines the values of \( n \).
Since \( n \) must be an integer (as indicated by \( n \in \mathbb{Z} \)), we find the integers that satisfy \( 1 < n < 12 \):
- The integers greater than 1 and less than 12 are: \( 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 \).
Thus, the elements of the set \( y \) are:
\[
y = \{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 \}
\]
1. The statement \( -3 \leq 9 \) is always true but does not affect the set definition.
2. We focus on the inequality \( 1 < n < 12 \), which defines the values of \( n \).
Since \( n \) must be an integer (as indicated by \( n \in \mathbb{Z} \)), we find the integers that satisfy \( 1 < n < 12 \):
- The integers greater than 1 and less than 12 are: \( 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 \).
Thus, the elements of the set \( y \) are:
\[
y = \{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 \}
\]