To find all subsets of the set [tex]\(\{3, 7, 8\}\)[/tex], we need to consider all possible combinations of its elements, including the empty set and the set itself. Here’s a step-by-step breakdown of how we can find these subsets:
1. Consider the empty set:
- An empty subset is always a subset of any set.
[tex]\[\emptyset\][/tex]
2. Consider subsets with one element:
- Each element in the original set can form a subset by itself.
[tex]\[\{3\}, \{7\}, \{8\}\][/tex]
3. Consider subsets with two elements:
- We can pair each element with every other element.
[tex]\[\{3, 7\}, \{3, 8\}, \{7, 8\}\][/tex]
4. Consider the subset containing all three elements:
- The full set is always a subset of itself.
[tex]\[\{3, 7, 8\}\][/tex]
Combining all these subsets, we get:
[tex]\[
\emptyset, \{3\}, \{7\}, \{8\}, \{3, 7\}, \{3, 8\}, \{7, 8\}, \{3, 7, 8\}
\][/tex]
Therefore, the subsets of the set [tex]\(\{3, 7, 8\}\)[/tex] are:
[tex]\[ \emptyset, \{3\}, \{7\}, \{8\}, \{3, 7\}, \{3, 8\}, \{7, 8\}, \{3, 7, 8\} \][/tex]
