Let U={h, i, j, k, l, m, n} and A = {i, k, m, n}. Use the listing method to write the set A'.
Answer (2)
Identify the universal set U and the subset A .
Determine elements in U that are not in A .
List these elements to form the complement A ′ .
The complement of A is { h , j , l } .
Explanation
Understanding the Problem We are given the universal set U = { h , i , j , k , l , m , n } and the set A = { i , k , m , n } . We want to find the complement of A , denoted by A ′ , which contains all elements in U that are not in A .
Finding the Complement To find A ′ , we look for the elements in U that are not in A . Comparing the two sets, we see that the elements h , j , and l are in U but not in A .
Listing the Elements Therefore, the complement of A is A ′ = { h , j , l } .
Examples
In set theory, understanding complements helps in database queries. For instance, if a database contains all customer IDs (U) and a subset represents premium members (A), the complement (A') identifies non-premium members. This is crucial for targeted marketing or service differentiation.
The complement of the set A within the universal set U is A' = {h, j, l}, which includes all elements in U not found in A. We identified the specific elements by comparing both sets. Thus, A' represents h, j, and l as the elements not included in A.
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