To determine the intersection of sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex], we need to identify the elements that are common to both sets.
Let's list out the elements of each set:
- Set [tex]\( C \)[/tex] consists of the elements: [tex]\( \{0, 1, 3, 10\} \)[/tex]
- Set [tex]\( D \)[/tex] consists of the elements: [tex]\( \{2, 4, 6, 8, 10\} \)[/tex]
The intersection of two sets, denoted [tex]\( C \cap D \)[/tex], includes all elements that are present in both sets.
Comparing the elements, we see that:
- The element 0 is in set [tex]\( C \)[/tex] but not in set [tex]\( D \)[/tex].
- The element 1 is in set [tex]\( C \)[/tex] but not in set [tex]\( D \)[/tex].
- The element 3 is in set [tex]\( C \)[/tex] but not in set [tex]\( D \)[/tex].
- The element 10 is in both set [tex]\( C \)[/tex] and set [tex]\( D \)[/tex].
No other elements are common to both sets.
Thus, the intersection of sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex] is:
[tex]\[ C \cap D = \{10\} \][/tex]
Therefore, the answer is:
[tex]\[
\boxed{10}
\][/tex]
