What is the different between A union B and {A union B}

Answer 1

In set theory, the expressions \( A \cup B \) and \( { A \cup B } \) represent two different concepts.

1. \( A \cup B \): This denotes the union of sets \( A \) and \( B \). The union of two sets is a new set that contains all the elements from both \( A \) and \( B \), without duplicates. For example, if \( A = {1, 2, 3} \) and \( B = {3, 4, 5} \), then \( A \cup B = {1, 2, 3, 4, 5} \).

2. \( { A \cup B } \): This notation describes a set containing a single element, which is itself the union of \( A \) and \( B \). The braces indicate that we are creating a set with one item, which is the whole union of \( A \) and \( B \). Using the previous example, \( { A \cup B } = { {1, 2, 3, 4, 5} } \), meaning we have a set whose only element is the set obtained from the union of \( A \) and \( B \).

In summary:

• \( A \cup B \) results in a set with all elements from both sets.
• \( { A \cup B } \) results in a set with one element, which is the set that resulted from the union \( A \cup B \).