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)

**(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**

*___*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