Let's first process the given set and operation. We have the set [tex]\( b = \{2, 4, 6, 8\} \)[/tex].
The operation [tex]\( \Delta \)[/tex] is defined as [tex]\( x \Delta y = x + 4 \)[/tex].
However, it appears that we are applying the operation in such a way that it affects each element independently. This can be interpreted as adding 4 to each element in the set [tex]\( b \)[/tex]. Let's proceed with this step-by-step for each element in the set:
1. For [tex]\( x = 2 \)[/tex]:
[tex]\[
2 \Delta 2 = 2 + 4 = 6
\][/tex]
2. For [tex]\( x = 4 \)[/tex]:
[tex]\[
4 \Delta 4 = 4 + 4 = 8
\][/tex]
3. For [tex]\( x = 6 \)[/tex]:
[tex]\[
6 \Delta 6 = 6 + 4 = 10
\][/tex]
4. For [tex]\( x = 8 \)[/tex]:
[tex]\[
8 \Delta 8 = 8 + 4 = 12
\][/tex]
Combining all these results, we get the following set after applying the operation to each element:
[tex]\[
\{6, 8, 10, 12\}
\][/tex]
Therefore, the result of applying the operation [tex]\( x \Delta y = x + 4 \)[/tex] to each element of the set [tex]\( b = \{2, 4, 6, 8\} \)[/tex] is:
[tex]\[
\{6, 8, 10, 12\}
\][/tex]
