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Relations are a type of association that exists between two or more objects.

1) If A & B are two non empty sets then Cartesian product of A & B is_____ (1)
A × B = {( a ,b ):a,b ∈A}
A × B = {( a ,b ):a,b ∈B}
A × B = {( a ,b ):a,∈A and b ∈B}
A × B = {( a ,b ):b ∈A and a∈B}

2) If set A contains n elements , set B contains m elements then number of elements in
A × B is __ (1)
m + n
m – n
m.n
m/n

3) If A,B and C are three sets and B C then _ (1)
a)A × B = A × C
b) A × B A × C
c)A × B A × A
d)A × C A × B

4) If A,B and C are three sets (A –B) × C then _ (1)
a) ( A × C) – (B × C)
b)(A × C)∪ (B× C)
c)(A × C)∩ (B× )
d)(A × C) (A × B)

5) If R_1 is a relation from A to B and R_2 is a relation from B to C, then (1)
a)M_(R_1 〖.R〗2 )=M(R_1 ) 〖+ M〗(R_2 ) b)M(R_1 〖.R〗2 )=M(R_1 ) 〖- M〗(R_2 ) c)M(R_1 〖.R〗2 )=M(R_1 ) 〖. M〗_(R_2 )
d) None of these

6) If R is a relation set A to Set B and R^’ is compliment of R then __ (1)
a)〖( R_1∪R_2)〗^’ =〖R_2〗^’∩〖R_1〗^’
b)(R_1∪R_2 )^’ =〖R_1〗^’∩〖R_2〗^’
c) 〖(R_1∪R_2)〗^’=〖R_1〗^’∪〖R_2〗^’
d)〖(R_1∪R_2)〗^’ =〖R_2〗^’∪〖R_1〗^’

7) If R is a relation from set A to set B and R^’ is compliment of R then (1)
a)〖( R_1∩R_2)〗^’ =〖R_2〗^’∩〖R_1〗^’
b)(R_1∩R_2 )^’ =〖R_1〗^’∩〖R_2〗^’
c) 〖(R_1∩R_2)〗^’=〖R_1〗^’∪〖R_2〗^’
d) 〖(R_1∩R_2)〗^’ =〖R_2〗^’∪〖R_1〗^’
8)If R is a relation from A to B then which is true ? (1)
a) R A × B and R^(-1) A × B
b)R A × BandR^(-1) B× A
c)R B× AandR^(-1) A × B
d)R B× AandR^(-1) B× A

9) Relation R on set A is antisymmetric if (1)
a)∀a ∈ R (a, a) ∈R
b)If (a, b) ∈R⇒(b, a) ∈R
c)If (a, b) ∈Rand (b, a) ∈R⇒ a=b
d)If (a, b) ∈Rand (b, a) ∈R⇒ a≠b

10)Relation R on set A is symmetric if (1)
a)∀ a ∈ A aRa
b) If aRb⇒ bRa
c)If aRb⇒ bRa⇒a=b
d) If aRb⇒ bRa⇒a≠b

11)Relation R on set A is reflexive if (1)
a)∀ a ∈ A aRa
b)If aRb⇒ bRa
c)If aRb⇒ bRa⇒a=b
d) If aRb⇒ bRa⇒a ≠b

12) Which is not Antisymmetric relation? (1)
a)Subset Relation
b) Les than or equal to relation
c)Greater than or equal to relation
d) On a set of integers I
R ={(a,b);a/b}

13)If R is a relation on a set A, then R is a partial ordered relation on A iff______ (1)
a) Ris reflexiveandsymmetric
b)Ris reflexiveandAntisymmetric
c)Ris reflexive, symmetricand transitive
d) R is reflexive , Antisymmetric and transitive

14)If R is a relation on a set A, then R is a equivalence relation on A iff______ (1)
a) Ris reflexiveand symmetric
b)Ris reflexiveandAntisymmetric
c) R is reflexive, symmetric and transitive
d) R is reflexive , Antisymmetric and transitive

15) If A = (1,2,3) and R on A is defined by R={(1,1),(2,2),(3,3)} then R is _ (1)
a) R is reflexive
b)Ris symmetric
c) R is transitive
d) R is Antisymmetric

16) If A=(1,2,3)and R on A is defined by R={(1,2),(2,1)(2,2),(1,1)} then R is _(2)
a) reflexiveand symmetric
b)transitiveandAntisymmetric
c) symmetric and transitive
d) reflexive and transitive

17)If A=(a,b,c)and R on A is defined by R={(a,b),(a,c)(b,c)} then R is _ (2)
a) reflexiveand symmetric
b) transitive and Antisymmetric
c) symmetric and transitive
d) reflexive and transitive

18) If s={(a,b);a,b ∈I } and (a,b) R (c,d) iff a+d = b+c then _ (4)
a) R is equivalence relation
b) R is partial order relation
c) R is reflexive,transitive but not symmetric
d) none of these

19) If N is a set of natural numbers and S={(a,b);a,b∈N } and (a,b) R(c,d)iff ad=bc then__________ (4)

``````R is a partial ordered relation
R is a equivalence relation
R is reflexive, symmetricbut not  transitive
none of these``````

20) If I is the set of all integers and a R b iff a+b is an even integer then _ (4) a) R is reflexivebut not symmetric b) R is not reflexivebut symmetric c) R is a equivalence relation d)none of these 21)If I is the set of all integersandR is a relation on a set I R ={(a,b);a/b} then (4)
a) R is reflexivebut not transitive
b) R is a equivalence relation
c)R is partial order relation
d)R is reflexive, transitive but not Antisymmetric
22) A lattice is a Poset (A,≤) in which every subset (a,b) of A has (1)
a) a least upper bound
b)a greatest lower bound
c) lub as well as glb
d) None of these
23) If A = {2,3,5,6,10,15,30} and a R b iff a/b then maximal element of A is (1) a)15 b) 10 c) 30 d) All of the above 24) If A = {2,3,5,6,10,15,30,45}and a R b iff a/b,lub of 2 & 5 is ___
(1)
a) 10
b) 6
c) 30
d) All of the above
24)If A = {2,3,5,6,10,15,30,45}and a R b iff a/b , upper bounds of 2& 3 are_____ (1)
a)6
b) 30
c) 6 & 30 both
d) None of these

25)If A = {2,3,5,6,10,15,30,45}, lub of2& 3 are________ (1)
a)6
b) 30
c) Both a) & b)
d) None of these
26)If A = {2,3,5,6,10,15,30,45}, glb of 30 & 45 are _ (1)
a)3
b) 5
c) 15
d) all of the above
27)If A = {2,3,5,6,10,15,30,45} and a R b iff a/b then (A,R) is
(2)
a) lattice
b) Poset but not lattice
c) Poset in which every pair has greatest lower bound
d)Poset in which every pair has least upper bound
28) If I is the set of integers and a R b iff a + b is an odd integer then_______ (2)
a) R is reflexive
b) R is symmetric
c) R is transitive
d) R is antisymmetric
29) If A = { 2, 3, 5, 6, 10, 15, 30} and a R b iff a/b then (A,R) is__________ (2)
a) lattice
b) poset in which every pair has glb
c) poset in which every pair has lub
d) none of these
30) S = {1, 2, 3} ans P(S) is power set of S also A R B iff A is subset of B then
(P(s),R) is a _ (2)
a)lattice
b)poset but not lattice
c)poset without glb
d)poset without lub
31) If S = { 1, 3, 5, 15, 30} and a R b iff a/b then chains of S are____ (2)
a) {1, 3, 5, 15}
b) {1, 3, 15, 30}
c) {1, 5, 15, 30}
d) {1, 3, 15, 30} and {1, 5, 15, 30} both

32)if S = {1, 2, 3}, P(S) is power set of S and A R B iff A is subset of B, then____ (4)
a) R is partial ordered relation
b) R is equivalence relation
c) R is reflexive, transitive but not antisymmetric
d) R is reflexive but not transitive
33) If A is the set of triangles in 2D plane and R is a relation defined on A such that
a R b iff a and b are congruent then___________ (4)
R is equivalence relation
R is partial ordered relation
R is symmetric but neither reflexive nor transitive
R is antisymmetric but neither reflexive nor transitive
34) If A = {a, b, c} and R on A defined by R = {(a,b),(a,c),(b,c)} then R is_____ (2)
a) reflexive and symmetric
b) Antisymmetric and transitive
c) reflexive and transitive
d) symmetric and transitive
35) If R and S are equivalence relation on a set A then which is not true? (2)
a) R ∩ S is an equivalence relation
b) R ∪ S is need not be an equivalence relation
c) R ∪ S is an equivalence relation
d) R ∩ S is an equivalence relation but
R ∪ S is need not be an equivalence relation