[see also: member, ingredient, feature, detail]
We shall call the elements of such a chain links.
Computing $f(y)$ can be done by enumerating $A(y)$ and testing each element for membership in $C$.
Two consecutive elements do not belong both to $A$ or both to $B$.
a 3-element set
Go to the list of words starting with: a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
y
z