To find [tex]\( n(A) \)[/tex], the number of elements in set [tex]\( A \)[/tex], where set [tex]\( A \)[/tex] consists of all integers between [tex]\(-11\)[/tex] and [tex]\(11\)[/tex] inclusive, we proceed as follows:
1. Identify the Range of Elements:
- The smallest integer in the set [tex]\( A \)[/tex] is [tex]\(-11\)[/tex].
- The largest integer in the set [tex]\( A \)[/tex] is [tex]\(11\)[/tex].
2. Number of Elements Calculation:
- To count the number of integers from [tex]\(-11\)[/tex] to [tex]\(11\)[/tex] inclusive, we can consider the endpoints and count all integers in this range.
3. Count the Integers:
- If we have a range from [tex]\( -11 \)[/tex] to [tex]\( 11 \)[/tex], it includes both [tex]\(-11\)[/tex] and [tex]\(11\)[/tex] as well as all integers in between.
4. Determine the Total Count:
- The count of integers from [tex]\(-11\)[/tex] to [tex]\(11\)[/tex] is equal to the total number of integers.
Therefore, the number of elements in the set [tex]\( A \)[/tex], denoted as [tex]\( n(A) \)[/tex], is:
[tex]\[ n(A) = 23 \][/tex]
Thus, the value of [tex]\( n(A) \)[/tex] is [tex]\( 23 \)[/tex].
