Discrete Mathematics
by
Meri Dedania
Assistant Professor
MCA department
Atmiya Institute of Technology & Science
Yogidham Gurukul
Rajkot
Prepared By
Meri Dedania (AITS)
Question Bank
of
POSET
Prepared By
Meri Dedania (AITS)
1.
2.
3.
Consider the relation of divisibility ‘|’ of
the set Z of integers. Is the relation an
ordering of Z?
Consider P(S) as the power set, i.e. the
set of all subsets of a given set S.then
investigate (P(S),) as a partially order set
,in which the symbol  denotes the
relation of set inclusion
Give an example of R which is both a
partial ordering relation and equivalence
relation
Prepared By
Meri Dedania (AITS)
4.
5.
6.
Let R be a binary relation on the set of all
positive integers such that R = {(a,b) : a-b
is an odd integer}. Investigate the relation
R for reflexive , symmetric , antisymmetric
,transitive and also R is partial ordering
relation?
If a relation R is transitive , then prove
that its inverse relation R-1 is also
transitive.
Let A={1,2,3,4} and consider the relation
R={(1,1),(1,2),(1,3),(2,2),(2,4),(3,3),(3,4),(1,
4),(4,4)}.show that R is partial ordering
and draw its Hasse diagram.
Prepared By
Meri Dedania (AITS)
7.
Draw the Hasse Diagram of the following
POSETs
1.
2.
3.
4.
8.
9.
<{1,2,3,4,6,9},|>
<{3,6,12,36,72},|>
<{2,3,4,9,12,18},|>
<{2,3,5,30,60,120,180,360},|>
Let A = {1,2,3,4,12} be defined by the
partial order of divisibility on A, that is if a
and b  A , a ≤ b iff a | b. draw the Hasse
diagram of the POSET <A, ≤>
Let S = {1,2,3} and A = P(S). Draw the
Hasse diagram of the POSET with the
partial order  (Inclusion)
Prepared By
Meri Dedania (AITS)
10.
Consider N = {1,2,3,……} be ordered by
divisibility. State whether each of the
following subsets of N is linearly ordered
1.
2.
3.
4.
5.
11.
{16,4,2}
{3,2,15}
{2,4,8,12}
{6}
{5,15,30}
Let dm denote the set of divisor of m
ordered by divisibility. Draw the Hasse
diagrams of
1.
2.
3.
d15
d16
d17
Prepared By
Meri Dedania (AITS)
12.
Find two incomparable elements in the
following POSETs
1. <S{0,1,2},>
2. <{1,2,4,6,8},|>
13.
Let D100 = {1,2,4,5,10,20,25,50,100}
whose all the elements are divisors of 100.
Let the relation ≤ be the relation |
(divides) be a partial ordering on D100
1.
2.
3.
4.
Determine the GLB of B where B = {10,20}
Determine the LUB of B where B = {10,20}
Determine the GLB of B where B = {5,10,20,25}
Determine the LUB of B where B = {5,10,20,25}
Prepared By
Meri Dedania (AITS)
14.
Draw the Hasse diagram for the “Less
than or equal to” relation on the set A =
{0,2,5,10,11,15}
15.
Draw the Hasse diagram for divisibility on
the following Sets
1.
2.
3.
4.
{1,2,3,4,5,6,7,8}
{1,2,3,5,7,11,13}
{1,2,3,6,12,24,36,48}
{1,2,4,8,16,32,64}
Prepared By
Meri Dedania (AITS)