To find the union of two sets [tex]\( C \)[/tex] and [tex]\( A \)[/tex], we follow these steps:
1. Identify the Elements of Each Set:
- Set [tex]\( C \)[/tex]: [tex]\(\{-3, 1, 5, 9\}\)[/tex]
- Set [tex]\( A \)[/tex]: [tex]\(\{-1, 3, 7\}\)[/tex]
2. Combine the Elements:
- We need to create a new set that contains all the unique elements from both sets [tex]\( C \)[/tex] and [tex]\( A \)[/tex].
3. List All Unique Elements:
- From set [tex]\( C \)[/tex] we have: [tex]\(-3, 1, 5, 9\)[/tex]
- From set [tex]\( A \)[/tex] we have: [tex]\(-1, 3, 7\)[/tex]
4. Form the Union of Sets:
- The union of sets [tex]\( C \)[/tex] and [tex]\( A \)[/tex] will have all these elements combined: [tex]\(-3, -1, 1, 3, 5, 7, 9\)[/tex]
5. Order the Elements:
- The elements in a set are often listed in ascending order to make it easier to understand.
Thus, the union [tex]\( C \cup A \)[/tex] results in the set:
[tex]\[ C \cup A = \{-3, -1, 1, 3, 5, 7, 9\} \][/tex]
So, [tex]\( C \cup A \)[/tex] is [tex]\((-3, -1, 1, 3, 5, 7, 9)\)[/tex].
