Discrete structures

Discrete Mathematics Chapter-2 (Relations), HW # 2

Directions: Answer all questions and double check your answers. After you feel comfortable with your answers, go to the content folder and click on HW-2_Relations to post your answers on blackboard. Make sure to submit your answers before the due date, you also need to allow yourself enough time (60 to 90 minutes) to submit your answers. When you start you must complete answering all questions. Questions and answers will be in the forms of True/False, Multiple Choice, and multiple answers. This will allow you to compare the answers you have with the different options on blackboard. Notice questions on blackboard may not have matching numbers with the following questions. Some of the following questions could be broken into multiple questions.

Q-1, 2, 3) For each of the following sets S, determine the number of possible relations on S (just as a power of 2, i.e. 2m ) :

Q-4, 5, 6) For each of the following sets A and B, determine the number of relations from A to B (just as a power of 2):

Q-7,8) Consider the following Relations on the set Determine the relations R and S in terms of ordered pairs for each of the corresponding directed graph. An arrow from a to b means a relates to b and the relation is represented by the ordered pair (a, b).

Q-9,10, 11, 12) Use these Relations on the set as viewed in Matrix form for questions Q9 through Q12.

Write the names of all those Relations satisfying the following properties (write in NONE if there are none):

Q9. Reflexive?

Q10. Symmetric?

Q11. Transitive?

Q12. Equivalence Relation?