Question

Find the set Upper A union empty set.
Upper U equals StartSet 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 EndSet
Upper A equals StartSet 3 comma 5 comma 6 comma 7 EndSet
Question content area bottom
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
Upper A union empty set equalsStartSet nothing EndSet
  
​(Use a comma to separate answers as​ needed.)
B.
Upper A union empty set is the empty set.

Answer 1

To find the union of set \( A \) and the empty set, we need to recall the definition of the union of two sets. The union of two sets consists of all elements that are in either set.

In this case, set \( A \) is given as:
\[ A = \{ 3, 5, 6, 7 \} \]
and the empty set is:
\[ \emptyset = \{ \} \]

The union of \( A \) and the empty set is:
\[ A \cup \emptyset = \{ 3, 5, 6, 7 \} \]

Since adding an empty set does not change the contents of the other set, we conclude:
\[ A \cup \emptyset = A \]

So, \( A \cup \emptyset = \{ 3, 5, 6, 7 \} \).

Now, looking at the choices:

A. \( A \cup \emptyset = \{ \} \) (the empty set)

B. \( A \cup \emptyset \) is the empty set.

Neither choice A nor B is correct since the union equals \( \{ 3, 5, 6, 7 \} \).

Thus, if needing to select from the given options, you should clarify the correct answer, which is:
\[ A \cup \emptyset = A = \{ 3, 5, 6, 7 \} \]