M131 Practice Quiz 2
1) Let R be an equivalence relation whose equivalence classes are
A1={0,3,4}, A2={1} , A3={2} then the ordered pairs of R are:
a. {(0,0) ,(0,3) ,(0,4), (3,3),(3,4) ,(1,1),(2,2)}
b. None
c. {(0,0) ,(0,3) ,(0,4),(3,0),(3,3),(3,4),(4,0),(4,3),(4,4),(1,1),(2,2)}
d. {(0,0),(0,1) , (1,0),(3,0) , (0,3) ,(0,4) ,(4,0) ,(3,4) ,(2,2)}
e. {(0,0),(0,1) , (1,0) ,(1,1) , (2,2) ,(3,0) , (0,3) ,(3,4) ,(4,3)}
2) Let A = {1,2} , B = {3,4,5} and C = {6,7} , If R is a relation from A to B
and S a relation from B to C represented by
:
and
then SoR is the relation :
a. C×A
b. None
c. {(1,6),(2,7)}
d. A×C
e. {(2,6),(1,7)}
3) Let R be the relation on the set {0,1,2,3} containing the ordered pairs
(0,1) , (1,1) , (1,2) , (2,0),(2,2) and (3,0).The transitive closure of R is:
a. {(0,0) ,(0,1),(1,1),(1,2),(2,0),(2,2),(3,0),(3,3)}
b. {(0,1),(1,1),(1,2),(2,0),(2,2),(3,0)}
c. {(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2),(3,0),(3,1)}
d. {(0,1) ,(0,2),(0,3),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2),(3,0)}
e. None
4) The relation R = {(1,1) , (1,2) (2,2) ,(2,1),(3,3),(3,4),(4,3)} defined on the
set {1,2,3,4} is :
a. symmetric and not transitive
b. None
c. Reflexive and not symmetric
d. symmetric and transitive
e. Reflexive and not transitive
5) The relation S on the set of real numbers given by x S y ⇔ x ≥ y is :
a. not transitive
b. Reflexive and antisymmetric
c. not anti symmetric
d. None
e. not reflexive
6) Let S be the relation defined on the set of positive integers by a S b ⇔
a divides b. Then S is:
a. not symmetric
b. an equivalence relation
c. not antisymmetric
d. partial order
7) The true proposition is :
a. An undirected graph has an even number of vertices of even degree
b. An undirected graph has an even number of vertices of odd degree
c. An undirected graph has an odd number of vertices of odd degree
d. An undirected graph has an odd number of vertices of even degree
e. none
8) The ordered pairs in the relation on {1,2,3} corresponding to the
matrix
a. (1,1) , (1,2) , (2,2) , (3,3)
b. (1,2) , (2,2) , (3,2) ,
c. (1,1) , (1,3) , (2,2) , (3,1) , (3,3)
d. None
e. (1,1) , (1,2) , (1,3) , (2,1) , (2,3) , (3,1)
9) Let G = (V,E) be a graph with directed edges .Then the true
proposition is :
a. ∑ deg-(v) = 2|E|
u∈v
b. ∑ deg-(v) ≠ ∑ deg+(v)
u∈v
u∈v
c. ∑ deg-(v) = |E|
u∈v
d. ∑ deg+(v) = 2|E|
u∈v
e. none
10) The number of edges of the complete bipartite graph K 4,5 is
a. 1
b. 9
c. 10
d. none
e. 20
Quiz script provided by
JavaScriptKit.com