reflexive, symmetric, antisymmetric, transitive?

For each of these binary relations, determine whether they are reflexive, symmetric,

antisymmetric, transitive. Give reasons for your answers and state whether or not they

form order relations or equivalence relations.

On the set {audi, ford, bmw, mercedes}, the relation

{(audi, audi), (audi, bmw), (bmw, bmw), (ford, ford), (mercedes,mercedes),

(audi, mercedes), (audi, ford), (bmw, ford), (mercedes, ford) }.

Let F be the set of all possible filenames consisting of character strings of at

least one character. The relation R contains all pairs of names (name1, name2)

where the first eight characters of name1 are the same as the first eight

characters of name2, or if name1 and name 2 have fewer than eight characters

and are exactly the same.