To find [tex]\( A \sim B \)[/tex], we need to determine the set difference, which means we look for elements that are in set [tex]\( A \)[/tex] but not in set [tex]\( B \)[/tex].
Given:
[tex]\[ A = \{1, 2, 3, 4, 6\} \][/tex]
[tex]\[ B = \{1, 3, 4\} \][/tex]
Here's how we can find [tex]\( A \sim B \)[/tex]:
1. List the elements of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] separately:
[tex]\[ A = \{1, 2, 3, 4, 6\} \][/tex]
[tex]\[ B = \{1, 3, 4\} \][/tex]
2. Identify the elements in [tex]\( A \)[/tex] that are not in [tex]\( B \)[/tex]:
- The element [tex]\( 1 \)[/tex] is in [tex]\( A \)[/tex] but also in [tex]\( B \)[/tex], so it is not included in the set difference.
- The element [tex]\( 2 \)[/tex] is in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex], so it is included in the set difference.
- The element [tex]\( 3 \)[/tex] is in [tex]\( A \)[/tex] but also in [tex]\( B \)[/tex], so it is not included in the set difference.
- The element [tex]\( 4 \)[/tex] is in [tex]\( A \)[/tex] but also in [tex]\( B \)[/tex], so it is not included in the set difference.
- The element [tex]\( 6 \)[/tex] is in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex], so it is included in the set difference.
3. Create the set with the elements from [tex]\( A \)[/tex] that are not in [tex]\( B \)[/tex]:
[tex]\[ A \sim B = \{2, 6\} \][/tex]
Therefore, the set difference [tex]\( A \sim B \)[/tex] is:
[tex]\[ \{2, 6\} \][/tex]
