Question
List the elements of the set, y={n|n is the element is interger; -3 is less than n is less than or equal to 9 and 1is less than n Less 12
Answers
GPT-4o mini
To find the elements of the set \( y = \{ n \mid n \text{ is an integer; } -3 < n \leq 9 \text{ and } 1 < n < 12 \} \), we need to identify the integer values of \( n \) that satisfy both conditions.
1. The condition \( -3 < n \leq 9 \) means \( n \) can take any integer value greater than -3 and up to and including 9. The integers that satisfy this condition are:
\[
-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
\]
2. The condition \( 1 < n < 12 \) means \( n \) can take any integer value greater than 1 and less than 12. The integers that satisfy this condition are:
\[
2, 3, 4, 5, 6, 7, 8, 9, 10, 11
\]
Now, we need to find the intersection of the two sets derived from both conditions. The common integers from both conditions are:
\[
\{ 2, 3, 4, 5, 6, 7, 8, 9 \}
\]
Therefore, the elements of the set \( y \) are:
\[
y = \{ 2, 3, 4, 5, 6, 7, 8, 9 \}
\]
1. The condition \( -3 < n \leq 9 \) means \( n \) can take any integer value greater than -3 and up to and including 9. The integers that satisfy this condition are:
\[
-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
\]
2. The condition \( 1 < n < 12 \) means \( n \) can take any integer value greater than 1 and less than 12. The integers that satisfy this condition are:
\[
2, 3, 4, 5, 6, 7, 8, 9, 10, 11
\]
Now, we need to find the intersection of the two sets derived from both conditions. The common integers from both conditions are:
\[
\{ 2, 3, 4, 5, 6, 7, 8, 9 \}
\]
Therefore, the elements of the set \( y \) are:
\[
y = \{ 2, 3, 4, 5, 6, 7, 8, 9 \}
\]