Problem

Find the set $A \cup U$.
\[
\begin{array}{l}
U=\{1,2,3,4,5,6,7,8\} \\
A=\{5,6,7,8\}
\end{array}
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $A \cup U=\{\}$ (Use a comma to separate answers as needed.)
B. $A \cup \cup$ is the empty set.

Answer

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Answer

\(\boxed{A \cup U = \{1,2,3,4,5,6,7,8\}}\)

Steps

Step 1 :First, understand the meaning of the union of sets. The union of two sets A and U, denoted by A ∪ U, is the set of elements which are in A, in U, or in both A and U.

Step 2 :In this case, set A is {5,6,7,8} and set U is {1,2,3,4,5,6,7,8}.

Step 3 :The union of A and U includes all the elements that are in A, in U, or in both.

Step 4 :Since all elements of A are also in U, the union of A and U is just U.

Step 5 :So, A ∪ U = {1,2,3,4,5,6,7,8}.

Step 6 :Check the result: all elements of A and U are included in the union, so the answer is correct.

Step 7 :\(\boxed{A \cup U = \{1,2,3,4,5,6,7,8\}}\)

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