Sure, let's find [tex]\( A \backslash B \)[/tex], which represents the set of elements that are in set [tex]\( A \)[/tex] but not in set [tex]\( B \)[/tex].
Given:
[tex]\[ A = \{0, 2, 4, 6, 8\} \][/tex]
[tex]\[ B = \{1, 3, 5, 7, 9\} \][/tex]
To calculate [tex]\( A \backslash B \)[/tex], we need to find all the elements that are in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex].
Step-by-step:
1. List the elements of set [tex]\( A \)[/tex]: \{0, 2, 4, 6, 8\}.
2. List the elements of set [tex]\( B \)[/tex]: \{1, 3, 5, 7, 9\}.
3. Compare each element in [tex]\( A \)[/tex] to the elements in [tex]\( B \)[/tex].
- 0: Not in [tex]\( B \)[/tex]
- 2: Not in [tex]\( B \)[/tex]
- 4: Not in [tex]\( B \)[/tex]
- 6: Not in [tex]\( B \)[/tex]
- 8: Not in [tex]\( B \)[/tex]
Since none of the elements in [tex]\( A \)[/tex] are in [tex]\( B \)[/tex], all the elements of [tex]\( A \)[/tex] remain in the set difference.
Therefore, the set [tex]\( A \backslash B \)[/tex] is:
[tex]\[ \{0, 2, 4, 6, 8\} \][/tex]
So the solution is:
[tex]\[ A \backslash B = \{0, 2, 4, 6, 8\} \][/tex]
