Home / Arithmetic Aptitude / Sets, Relations and Functions :: Section-1

### Arithmetic Aptitude :: Sets, Relations and Functions

1.  Which of the following sets are null sets ?

2.  A. { } B. ø C. Both (a) and (b) D. {0}

3.  Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B = Ø Then (pick the TRUE statement)

4.  A. R is relexive and transitive B. R is an equivalence relation C. R is symmetric and not transitive D. R is not relexive and not symmetric

5.  The binary relation S = Φ (empty set) on set A = {1, 2,3} is

6.  A. transitive and relexive B. symmetric and relexive C. transitive and symmetric D. neither reflexive nor symmetric

7.  Number of subsets of a set of order three is

8.  A. 2 B. 4 C. 6 D. 8

9.  "n/m" means that n is a factor of m, then the relation T is

10.  A. relexive, transitive and not symmetric B. relexive, transitive and symmetric C. transitive and symmetric D. relexive and symmetric

11.  If R be a symmetric and transitvie relation on a set A, then

12.  A. R is not reflexive and hence not an equivalence relation B. R is reflexive and hence an equivalence relation C. R is reflexive and hence a partial order D. None of these

13.  Let P(S) denote the power set of set S. Which of the following is always TRUE ?

14.  A. S ∉ P(S) B. P(P(S)) = P(S) C. P(S)  ∩ S = P (S) D. P(S)  ∩ P(P(S))  = [ φ ]

15.  The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is

16.  A. 2 B. 4 C. 6 D. 8

17.  If A and B are sets and A∪ B= A ∩ B, then

18.  A. A = B B. A = Φ C. B = Φ D. none of these

19.  Let S be an infinite set and S1, S2, S3, ..., Sn be sets such that S1 ∪S2 ∪S3∪ .......Sn = S then

20.  A. atleast one of the sets Si is a finite set B. atleast one of the sets Si is an ininite set C. not more than one of the set Si can be inite D. none of these