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question let s be the set of all strings of english letters determine whether these relations are reflexive irreflexive
question a define a well-ordered setb describe an algorithm for producing a totally ordered set compatible with a given
question a show that every finite subset of a lattice has a greatest lower bound and a least upper boundb show that
question a define a latticeb give an example of a poset with five elements that is a lattice and an example of a poset
question a define a maximal element of a poset and the greatest element of a posetb give an example of a poset that has
question a explain how to construct the hasse diagram of a partial order on a finite setb draw the hasse diagram of the
question a give an example to show that the transitive closure of the symmetric closure of a relation is not
question a what is a reflexive relationb what is a symmetric relationc what is an antisymmetric relationd what is a
question a what is a relation on a setb how many relations are there on a set with n
question find an ordering of the tasks of a software project if the hasse diagram for the tasks of the project is as
question schedule the tasks needed to build a house by specifying their order if the hasse diagram representing these
question find all compatible total orderings for the poset with the hasse diagram in exerciseexercise list all ordered
question a explain how an n-ary relation can be used to represent information about students at a universityb how can
question a explain how to use a zero-one matrix to represent a relation on a finite setb explain how to use the
question a explain how to use a directed graph to represent a relation on a finite setb explain how to use the directed
question a define the reflexive closure and the symmetric closure of a relationb how can you construct the reflexive
question a define the transitive closure of a relationb can the transitive closure of a relation be obtained by
question a define an equivalence relationb which relations on the set a b c d are equivalence relations and contain a b
question a show that congruence modulo m is an equivalence relation whenever m is a positive integerb show that the
question a what are the equivalence classes of an equivalence relationb what are the equivalence classes of the
question a define a partial orderingb show that the divisibility relation on the set of positive integers is a partial
question draw the hasse diagram for divisibility on the seta 1 2 3 4 5 6 7 8b 1 2 3 5 7 11 13c 1 2 3 6 12 24 36 48d 1 2
question answer these questions for the poset 1 2 4 1 2 1 4 2 4 3 4 1 3 4 2 3 4 subea find the maximal elementsb find
question give a poset that has za a minimal element but no maximal elementb a maximal element but no minimal elementc
question a show that there is exactly one greatest element of a poset if such an element existsb show that there is