01/06/2021
Yıldız Technical University/Control and Automation Department
KOM1062 Discrete Mathematics, Gr:2, Midterm-2
NOTE 1: The answer sheet must be uploaded YTU/Online platform before the exam-
slot closes. Otherwise, the evaluation will not be done. You have total of 75 minutes to
solve and upload the answer sheet.
NOTE 2: The answer sheet must be clear, organized, easy to read and understand and it
should be converted into a pdf file. Also, the related file should be named with your ID
information.
Ad:
Soyad:
Numara:
İmza:
1)(30 pnt.) Consider the relation of R= {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2),(3, 3)}
defined by the set of A={0,1,2,3}. Does this relation have equivalency property? Explain
with reasons.
2)(40 pnt.) Consider the partially ordering relation of
{( , ) | 'yi bö ler}
x y x y defined by the set
of
{3, 4, 6 , 7,1 1, 21, 24 , 36, 5 5, 72 , 77, 13 2}
S
.
a) Draw Hasse diagram.
b) Find the small and big elements.
c) If there are, find the smallest and biggest elements.
d) Is the poset of
{ , |}
S
a lattice or not? Explain with reasons.
3)(30 pnt.) Answer the following questions.
1.a)(15p.) Solve the recurrence relation = − − − with
= , = − and = .
1.b) (15p.) Find all solutions of the recurrence relation
=
−
+
+
.
