Certainly! Let's find the sets [tex]\( C \cup D \)[/tex] and [tex]\( C \cap D \)[/tex] step-by-step:
1. Union of Sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex] [tex]\( (C \cup D) \)[/tex]:
- The union of two sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex] includes all elements that are in either [tex]\( C \)[/tex], in [tex]\( D \)[/tex], or in both.
- Set [tex]\( C \)[/tex] is [tex]\(\{0, 1, 2\}\)[/tex]
- Set [tex]\( D \)[/tex] is [tex]\(\{2, 4, 6\}\)[/tex]
- Combining all elements from both sets without any duplicates, we get:
[tex]\[
C \cup D = \{0, 1, 2, 4, 6\}
\][/tex]
2. Intersection of Sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex] [tex]\( (C \cap D) \)[/tex]:
- The intersection of two sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex] includes only the elements that are common to both sets.
- Looking for common elements in [tex]\( C \)[/tex] and [tex]\( D \)[/tex]:
- In [tex]\( C = \{0, 1, 2\}\)[/tex]
- In [tex]\( D = \{2, 4, 6\}\)[/tex]
- The only element common to both [tex]\( C \)[/tex] and [tex]\( D \)[/tex] is [tex]\( 2 \)[/tex].
- Therefore, the intersection is:
[tex]\[
C \cap D = \{2\}
\][/tex]
Thus, the sets [tex]\( C \cup D \)[/tex] and [tex]\( C \cap D \)[/tex] are:
- [tex]\( C \cup D = \{0, 1, 2, 4, 6\} \)[/tex]
- [tex]\( C \cap D = \{2\} \)[/tex]
These are the union and intersection of the sets [tex]\( C \)[/tex] and [tex]\( D \)[/tex].
