To find the union of sets [tex]\( B \)[/tex] and [tex]\( C \)[/tex], denoted as [tex]\( B \cup C \)[/tex], we need to combine all unique elements from both sets. Let's list the elements of each set:
- Set [tex]\( B = \{ a, b, c, d \} \)[/tex]
- Set [tex]\( C = \{ 0, a, 2, b \} \)[/tex]
The union of two sets includes every element that is in either one of the sets or in both of them. In other words, it combines all elements from both sets without any duplication.
Let's combine the elements of [tex]\( B \)[/tex] and [tex]\( C \)[/tex]:
- From set [tex]\( B \)[/tex], we have [tex]\( a, b, c, \)[/tex] and [tex]\( d \)[/tex].
- From set [tex]\( C \)[/tex], we add the elements [tex]\( 0 \)[/tex] and [tex]\( 2 \)[/tex] to the combined set, but we do not add [tex]\( a \)[/tex] and [tex]\( b \)[/tex] again since they are already included.
Combining these, we get:
[tex]\[ B \cup C = \{ a, b, c, d, 0, 2 \} \][/tex]
Therefore, the correct answer is:
[tex]\[ \{ a, b, c, d, 0, 2 \} \][/tex]
