discrete math two exam one review

trail

a valid walk with no repeating edges

circuit

a closed valid walk w no repeating edges

path

an open valid walk with no repeating vertices

cycle

a closed valid trail with no repeating edges, vertices, and whose length is at least 1

a relation R on A is a partial order if…

is its reflexive, anti-symmetric, and transitive

total order

means any pair of elements are compatible

minimal

least to no of inbound arrows

maximal

least to no outbound arrows

hasse diagram

upward drawing, reflexivity and transitivity is assumed.

a equivalence relation of R is…

reflexive, symmetric, and transitive. denoted a ~ b

ex: you have the same bday as yourself. if you and jackie have the same bday, and jackie has the same bday as maria, then you have the same bday as maria

total order

all pair of elements are compatible