To determine the elements in the union of Sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex] (denoted as [tex]\(A \cup B\)[/tex]), we need to include all the unique elements that are present in either Set [tex]\(A\)[/tex], Set [tex]\(B\)[/tex], or both.
Given:
[tex]\[ A = \{\text{engineer, architect, teacher, attorney}\} \][/tex]
[tex]\[ B = \{\text{architect, teacher, mechanic}\} \][/tex]
The union of two sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex] will include each element that appears in either [tex]\(A\)[/tex] or [tex]\(B\)[/tex] without repetition. Let's list the elements:
1. From Set [tex]\(A\)[/tex]:
- engineer
- architect
- teacher
- attorney
2. From Set [tex]\(B\)[/tex]:
- architect (already included from Set [tex]\(A\)[/tex])
- teacher (already included from Set [tex]\(A\)[/tex])
- mechanic (new element)
Combining all unique elements from both sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we get:
[tex]\[ A \cup B = \{\text{engineer, architect, teacher, attorney, mechanic}\} \][/tex]
Thus, the elements in [tex]\(A \cup B\)[/tex] are:
[tex]\[ \{\text{engineer, architect, teacher, attorney, mechanic}\} \][/tex]
So, the correct answer from the given choices is:
[tex]\[ \{\text{engineer, architect, teacher, attorney, mechanic}\} \][/tex]
