1. Which of the following two relations is reflexive, irreflexive, transitive, antisym-
metric, symmetric, asymmetric, total, a preorder, a partial order, an equivalence
relation?
(1) A relation R₁ on the set of municipalities in South Tyrol is defined as follows:
town 1 (T1) is in relation with town 2 (T2) if the name of T1 does not come later
in the lexicographic order than the name of T2 (you may choose the Italian or the
German names, but fix your choice beforehand).
(2) On the same set of municipalities, another relation R₂ is defined as follows: T1
is in relation with T2 if the name of T1 has at least as many letters as the name of
T2.