v
in
N
(
A
∪
B
)
⇔
v
is adjacent to a vertex in
A
∪
B
⇔
v
is adjacent to a vertex in
A
or
v
is adjacent to a vertex in
B
(since each vertex in
A
∪
B
is either in
A
or in
B
)
⇔
v
∈
N
(
A
) ∪
N
(
B
)