please answer all the question listed in the pdf file. Discrete Mathematics
Chapter-2 (Relations), HW # 2

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?