Unit 22 Exercises

1. Which of the following are posets?

  1. ( Z,  =  )
  2. ( Z, neq.gif 
(901 bytes) )
  3. ( A collection of sets, subseteq.gif (874 bytes) ).

2. Draw the Hasse diagram for the divisibility relation on the following sets

    a) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

    b) {1, 2, 5, 8, 16, 32}

3. Answer the following questions concerning the poset ({{1}, {2}, {3}, {4}, {1, 3}, {1, 4}, {2, 4}, {3, 4}, {1, 2, 4}, {2, 3, 4}},  subseteq.gif (874 bytes) ).

  1. Find the maximal elements.
  2. Find the minimal elements.
  3. Is there a greatest element?
  4. Is there a least element?
  5. Find all upper bounds of {{2}, {4}}.
  6. Find the least upper bound of {{2}, {4}}, if it exists.
  7. Find all lower bounds of {{1, 2, 4}, {2, 3, 4}}
  8. Find the greatest lower bound of {{1, 2, 4}, {2, 3, 4}}, if it exists.

 

Answers for these exercises