To determine the intersection of the sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex], denoted as [tex]\( C \cap D \)[/tex], we need to identify the elements that both sets have in common.
Given:
[tex]\[ C = \{0, 1, 3, 10\} \][/tex]
[tex]\[ D = \{2, 4, 6, 8, 10\} \][/tex]
The intersection [tex]\( C \cap D \)[/tex] includes only those elements which are present in both sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex].
Let’s compare the elements of both sets one by one:
1. The element [tex]\( 0 \)[/tex] is in set [tex]\( C \)[/tex] but not in set [tex]\( D \)[/tex].
2. The element [tex]\( 1 \)[/tex] is in set [tex]\( C \)[/tex] but not in set [tex]\( D \)[/tex].
3. The element [tex]\( 3 \)[/tex] is in set [tex]\( C \)[/tex] but not in set [tex]\( D \)[/tex].
4. The element [tex]\( 10 \)[/tex] is in set [tex]\( C \)[/tex] and also in set [tex]\( D \)[/tex].
Since the only element common to both sets is [tex]\( 10 \)[/tex], the intersection [tex]\( C \cap D \)[/tex] is:
[tex]\[ C \cap D = \{10\} \][/tex]
Thus, the solution to the intersection is:
[tex]\[ \boxed{10} \][/tex]
