4.13 The purpose of this exercise is to give some examples of cliques based on Figures 4.3 and 4.4. Let T = ℤ2 and consider the neighborhood structures generated by translates {(basic,1)

t = t + (basic,1)

, t ∈ ℤ2} of the first-order basic neighborhood (basic,1) and by translates of the first-order full neighborhood (full,2) defined in Section 4.4.

(a) For the first-order basic neighborhood structure, show that the cliques are given by

(i) Singletons {t}, t ∈ ℤ2.

(ii) Horizontal and vertical two-point segments {t, t + (1,0)} and

{t, t + (0,1)}