To determine the relationship between set [tex]\( C \)[/tex] and set [tex]\( D \)[/tex], we need to examine the elements of each set.
1. Set [tex]\( C \)[/tex] is given as [tex]\( \{1, 2, 3, 4, 5, 6, 7, 8\} \)[/tex].
2. Set [tex]\( D \)[/tex] is given as [tex]\( \{2, 4, 6, 8\} \)[/tex].
To find the relationship, let's see if all elements of set [tex]\( D \)[/tex] are contained in set [tex]\( C \)[/tex]:
- The element 2 is in set [tex]\( C \)[/tex].
- The element 4 is in set [tex]\( C \)[/tex].
- The element 6 is in set [tex]\( C \)[/tex].
- The element 8 is in set [tex]\( C \)[/tex].
Since all elements of set [tex]\( D \)[/tex] are contained in set [tex]\( C \)[/tex], set [tex]\( D \)[/tex] is a subset of set [tex]\( C \)[/tex].
We use the subset notation ([tex]\(\subseteq\)[/tex]) to indicate this relationship. Therefore, the relationship between set [tex]\( C \)[/tex] and set [tex]\( D \)[/tex] is:
[tex]\[ D \subseteq C \][/tex]
So, the correct notation to show the relationship between sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex] is:
[tex]\[ \boxed{D \subseteq C} \][/tex]
