Exercises
Q1: Determine all the partial orders and their Hasse diagrams on the set L = {a, b, c}. Which of them are chains?
Q2: Give an example of a poset which has exactly one maximal element but does not have a greatest element.
Q3: Let (R, <=) be the poset of all real numbers and let A = {x in R | x^3 < 3}. Is there an upper bound (or lower bound) or a supremum (or infimum) of A?
Q4: Show that the examples in 1.12 are really lattices and prove the indicated properties.