Answer
$A\cup (A\cup B)'=\{23, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71\}$
Work Step by Step
In the diagram $(A\cup B)$ is a set of all elements inside the circle for $A$, the circle for $B$, or in both the circle for $A$ and the circle for $B$.
$(A\cup B)'$ is a set of elements in $U$ (the whole diagram) but not in $(A\cup B)$.
We can see that those elements are:
$(A\cup B)' = \{53, 59, 61, 67, 71\}$
The elements in $A$ from the diagram are:
$A=\{23, 29, 31, 37, 41, 43\}$
Therefore:
$A\cup (A\cup B)'=\{23, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71\}$
