To find the intersection and union of the sets [tex]\( D \)[/tex] and [tex]\( J \)[/tex], we need to follow these steps:
1. Intersection of [tex]\( D \)[/tex] and [tex]\( J \)[/tex]:
The intersection of two sets includes only the elements that are present in both sets.
- Set [tex]\( D \)[/tex] is [tex]\(\{-2, 2, 4, 7\}\)[/tex]
- Set [tex]\( J \)[/tex] is [tex]\(\{-2, -1, 0, 8\}\)[/tex]
We look for the common elements in both sets:
Elements in [tex]\( D \)[/tex] are: [tex]\(-2, 2, 4, 7\)[/tex]
Elements in [tex]\( J \)[/tex] are: [tex]\(-2, -1, 0, 8\)[/tex]
The common element in both sets is [tex]\(-2\)[/tex].
Therefore, the intersection [tex]\( D \cap J \)[/tex] is:
[tex]\[
D \cap J = \{-2\}
\][/tex]
2. Union of [tex]\( D \)[/tex] and [tex]\( J \)[/tex]:
The union of two sets includes all the elements that are present in either set, without repetition.
- Set [tex]\( D \)[/tex] is [tex]\(\{-2, 2, 4, 7\}\)[/tex]
- Set [tex]\( J \)[/tex] is [tex]\(\{-2, -1, 0, 8\}\)[/tex]
We combine all elements from both sets, removing duplicates:
Elements from [tex]\( D \)[/tex] are: [tex]\(-2, 2, 4, 7\)[/tex]
Elements from [tex]\( J \)[/tex] are: [tex]\(-2, -1, 0, 8\)[/tex]
Combining these elements without repetition, we get:
[tex]\(-2, 2, 4, 7, -1, 0, 8\)[/tex]
Therefore, the union [tex]\( D \cup J \)[/tex] is:
[tex]\[
D \cup J = \{0, 2, 4, 7, 8, -1, -2\}
\][/tex]
Thus, the intersection and union of the sets [tex]\( D \)[/tex] and [tex]\( J \)[/tex] are:
[tex]\[
D \cap J = \{-2\}
\][/tex]
[tex]\[
D \cup J = \{0, 2, 4, 7, 8, -1, -2\}
\][/tex]
