Find the set $A \cup \varnothing$. \[ \begin{array}{l} U=\{1,2,3,4,5,6,7,8\} \\ A=\{3,4,6,7\} \end{array} \]

Step 1 ：Given the universal set \(U = \{1,2,3,4,5,6,7,8\}\) and the set \(A = \{3,4,6,7\}\).

Step 2 ：We are asked to find the union of set \(A\) and the empty set.

Step 3 ：The union of a set with the empty set is always the set itself.

Step 4 ：Therefore, the union of set \(A\) and the empty set is \(A\) itself.

Step 5 ：Final Answer: \(A \cup \varnothing = \boxed{\{3, 4, 6, 7\}}\)