To find the intersection of sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex], we need to determine which elements are common to both sets.
First, let's list the elements of each set:
- Set [tex]\( C \)[/tex] consists of [tex]\(\{0, 1, 3, 10\}\)[/tex].
- Set [tex]\( D \)[/tex] consists of [tex]\(\{2, 4, 6, 8, 10\}\)[/tex].
Next, we compare the elements of both sets and identify the elements present in both [tex]\( C \)[/tex] and [tex]\( D \)[/tex].
Starting with set [tex]\( C \)[/tex]:
- [tex]\( 0 \)[/tex] is in [tex]\( C \)[/tex] but not in [tex]\( D \)[/tex].
- [tex]\( 1 \)[/tex] is in [tex]\( C \)[/tex] but not in [tex]\( D \)[/tex].
- [tex]\( 3 \)[/tex] is in [tex]\( C \)[/tex] but not in [tex]\( D \)[/tex].
- [tex]\( 10 \)[/tex] is in both [tex]\( C \)[/tex] and [tex]\( D \)[/tex].
Similarly, let's check set [tex]\( D \)[/tex]:
- [tex]\( 2 \)[/tex] is in [tex]\( D \)[/tex] but not in [tex]\( C \)[/tex].
- [tex]\( 4 \)[/tex] is in [tex]\( D \)[/tex] but not in [tex]\( C \)[/tex].
- [tex]\( 6 \)[/tex] is in [tex]\( D \)[/tex] but not in [tex]\( C \)[/tex].
- [tex]\( 8 \)[/tex] is in [tex]\( D \)[/tex] but not in [tex]\( C \)[/tex].
- [tex]\( 10 \)[/tex] is in both [tex]\( D \)[/tex] and [tex]\( C \)[/tex].
From this comparison, we can see that the only element common to both sets is [tex]\( 10 \)[/tex].
Therefore, the intersection of sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex] is:
[tex]\[ C \cap D = \{10\} \][/tex]
