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Unit 1: Set Theory, Relation and Function - Practice Quiz

MTH136 — Discrete Structures 60 Questions
0 Correct 0 Wrong 60 Left
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1 Which of the following best describes a set?

sets Easy
A. A collection of similar equations
B. A well-defined collection of distinct objects
C. A random group of symbols
D. An ordered list of numbers

2 The set is written in which form?

description of a set Easy
A. Roster (tabular) form
B. Set-builder form
C. Interval form
D. Descriptive statement form

3 Which of the following represents the set-builder form of ?

description of a set Easy
A.
B.
C.
D.

4 A set containing no elements is called a/an:

types of sets Easy
A. Finite set
B. Singleton set
C. Empty set
D. Universal set

5 A set that contains exactly one element is known as a:

types of sets Easy
A. Singleton set
B. Finite set
C. Power set
D. Empty set

6 If , which of the following is a subset of ?

subsets Easy
A.
B.
C.
D.

7 The empty set is a subset of:

subsets Easy
A. Only the empty set
B. No set
C. Every set
D. Only infinite sets

8 If , how many elements does the power set have?

power set Easy
A.
B.
C.
D.

9 The power set of a set is the set of all:

power set Easy
A. Elements of
B. Subsets of
C. Supersets of
D. Proper subsets of only

10 If and , then is:

operation on sets (union, intersection and difference) Easy
A.
B.
C.
D.

11 If and , then is:

operation on sets (union, intersection and difference) Easy
A.
B.
C.
D.

12 If and , then is:

operation on sets (union, intersection and difference) Easy
A.
B.
C.
D.

13 In a Venn diagram, the overlapping region between two circles and represents:

Venn diagrams Easy
A.
B.
C.
D.

14 Which of the following is the commutative law for the union of sets?

laws of set theory Easy
A.
B.
C.
D.

15 According to De Morgan's law, equals:

laws of set theory Easy
A.
B.
C.
D.

16 If and , then is:

cartesian product of sets Easy
A.
B.
C.
D.

17 If and , then the number of elements in is:

cartesian product of sets Easy
A.
B.
C.
D.

18 A relation from set to set is a subset of:

relations Easy
A.
B.
C.
D.

19 A function assigns to each element of :

functions Easy
A. Exactly one element of
B. At least two elements of
C. No element of
D. All elements of

20 The value of the greatest integer function is:

some functions and their graphs (identity, polynomial, modulus function and greatest integer function) Easy
A.
B.
C.
D.

21 If a set has elements, then the number of elements in the power set of the power set of (i.e. ) when is:

power set Medium
A.
B.
C.
D.

22 For sets and , what is ?

operation on sets (union, intersection and difference) Medium
A.
B.
C.
D.

23 Which of the following sets is an infinite set?

types of sets Medium
A. The set of solutions of
B. The set of divisors of
C. The set of letters in the word MATHEMATICS
D. The set of all prime numbers

24 Using De Morgan's laws, is equal to:

laws of set theory Medium
A.
B.
C.
D.

25 If and , how many elements does contain, and which pair belongs to it?

cartesian product of sets Medium
A. elements, and belongs to it
B. elements, and belongs to it
C. elements, and belongs to it
D. elements, and belongs to it

26 The value of is:

greatest integer function Medium
A.
B.
C.
D.

27 Let be defined by . This function is:

one-one and onto functions Medium
A. Neither one-one nor onto
B. One-one but not onto
C. Onto but not one-one
D. Both one-one and onto

28 How many proper subsets does the set have?

subsets Medium
A.
B.
C.
D.

29 A relation is defined on as . This relation is:

relations Medium
A. Both reflexive and symmetric
B. Reflexive but not symmetric
C. Symmetric but not reflexive
D. Transitive but not reflexive

30 If , , and , then equals:

operation on sets (union, intersection and difference) Medium
A.
B.
C.
D.

31 The solution set of the inequality is:

modulus function Medium
A.
B.
C.
D.

32 If for , then equals:

functions Medium
A.
B.
C.
D.

33 In a class of students, play cricket and play football, and play both. How many students play neither game?

Venn diagrams Medium
A.
B.
C.
D.

34 The expression simplifies to:

laws of set theory Medium
A.
B.
C.
D.

35 The function given by is:

one-one and onto functions Medium
A. A bijection (one-one and onto)
B. Neither one-one nor onto
C. Onto but not one-one
D. One-one but not onto

36 If , then sets and are:

cartesian product of sets Medium
A.
B.
C.
D.

37 Which of the following is an element of the power set ?

power set Medium
A.
B.
C.
D.

38 The graph of the identity function is a straight line passing through the origin with slope:

some functions and their graphs (identity, polynomial, modulus function and greatest integer function) Medium
A.
B.
C. undefined
D.

39 The set written in roster form is:

description of a set Medium
A.
B.
C.
D.

40 If has elements and has elements, how many relations are possible from to ?

relations Medium
A.
B.
C.
D.

41 If is a set such that , where denotes the power set of , then the number of elements in is:

power set Hard
A.
B.
C.
D.

42 For a finite set with , the number of elements in that contain a fixed element is:

power set Hard
A.
B.
C.
D.

43 For sets , the symmetric difference . Which statement is always true?

operation on sets (union, intersection and difference) Hard
A.
B. always
C.
D.

44 Using set identities, simplify :

laws of set theory Hard
A.
B.
C.
D.

45 In a survey of people, like tea, like coffee, and like both. How many like neither tea nor coffee?

operation on sets (union, intersection and difference) Hard
A.
B.
C.
D.

46 If and , how many relations from to are there?

cartesian product of sets Hard
A.
B.
C.
D.

47 On the set , how many relations are both reflexive and symmetric?

relations Hard
A.
B.
C.
D.

48 A relation on is defined by is divisible by . Which property does NOT satisfy?

relations Hard
A. It is not symmetric
B. It is not reflexive
C. It is not transitive
D. It is not antisymmetric

49 How many onto (surjective) functions are there from a set with elements to a set with elements?

functions Hard
A.
B.
C.
D.

50 The function defined by is:

one-one and onto functions Hard
A. Onto but not one-one
B. Neither one-one nor onto
C. Both one-one and onto
D. One-one but not onto

51 For the greatest integer function, evaluate :

some functions and their graphs (identity, polynomial, modulus function and greatest integer function) Hard
A.
B.
C.
D.

52 The range of for is:

some functions and their graphs (identity, polynomial, modulus function and greatest integer function) Hard
A.
B.
C.
D.

53 Which of the following sets is finite?

types of sets Hard
A.
B.
C.
D.

54 The number of subsets of that contain at least one odd number is:

subsets Hard
A.
B.
C.
D.

55 In a class, study Math, study Physics, and study both. If students study neither, and percentages are of the total, how many students are in the class?

Venn diagrams Hard
A.
B.
C.
D.

56 If has elements and includes and , then which of the following could be the sets and ?

cartesian product of sets Hard
A.
B.
C.
D.

57 Let be . This function is:

one-one and onto functions Hard
A. A bijection
B. Onto but not one-one
C. Neither one-one nor onto
D. One-one but not onto

58 Which expression equals by De Morgan's and distributive laws?

laws of set theory Hard
A.
B.
C.
D.

59 The number of solutions of for real is:

some functions and their graphs (identity, polynomial, modulus function and greatest integer function) Hard
A. Exactly
B. Exactly
C. None
D. Infinitely many

60 On a set with elements, the number of relations that are reflexive is:

relations Hard
A.
B.
C.
D.
Next MCQ
Unit 2