The following Venn Diagram shows the sets A, B, C and the eight regions they form. We will use these region labels to discuss the sets.


The regions represented by
A', B, C
are as follows.
A' =
{i, ii, iv}
{iii, vi, vii, viii}
{iii, vi, vii}
{i, ii, iv, v}
{i, ii, iii, iv}
B =
{i, ii, iii, vi}
C =
{v, vi, vii}
{v, vi, viii}
{i, iii, iv, vii}
{i, ii, iii, iv}
{ii, v, vi}

To diagram
(A' ∩ B) ∪ C
, we first consider
(A' ∩ B)
because it is in parentheses. The set
(A' ∩ B)
is the intersection of A' and B, that is, the set of only those regions that appear in both sets.
A' ∩ B =
{iv, vii}
{iii, vi}
{iii, iv, v}
{ii, v}
{ii, v, vi}