Discrete Mathematics Questions and Answers PDF

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Discrete Mathematics Questions and Answers – Sets This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Sets”.

1. A __________ is an ordered collection of objects. a) Relation b) Function c) Set d) Proposition View Answer

Answer: c Explanation: By the definition of set. 2. The set O of odd positive integers less than 10 can be expressed by _____________ a) {1, 2, 3} b) {1, 3, 5, 7, 9} c) {1, 2, 5, 9} d) {1, 5, 7, 9, 11} View Answer

Answer: b Explanation: Odd numbers less than 10 is {1, 3, 5, 7, 9}. 3. Power set of empty set has exactly _________ subset. a) One b) Two c) Zero d) Three View Answer

Answer: a

Explanation: Power set of null set has exactly one subset which is empty set. 4. What is the Cartesian product of A = {1, 2} and B = {a, b}? a) {(1, a), (1, b), (2, a), (b, b)} b) {(1, 1), (2, 2), (a, a), (b, b)} c) {(1, a), (2, a), (1, b), (2, b)} d) {(1, 1), (a, a), (2, a), (1, b)} View Answer

Answer: c Explanation: A subset R of the Cartesian product A x B is a relation from the set A to the set B. 5. The Cartesian Product B x A is equal to the Cartesian product A x B. a) True b) False View Answer

Answer: b Explanation: Let A = {1, 2} and B = {a, b}. The Cartesian product A x B = {(1, a), (1, b), (2, a), (2, b)} and the Cartesian product B x A = {(a, 1), (a, 2), (b, 1), (b, 2)}. This is not equal to A x B. advertisement Video Player is loading. PauseUnmute Fullscreen VDO.AI 6. What is the cardinality of the set of odd positive integers less than 10? a) 10 b) 5 c) 3 d) 20 View Answer

Answer: b Explanation: Set S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}. Then, Cardinality of set S = |S| which is 5. 7. Which of the following two sets are equal? a) A = {1, 2} and B = {1} b) A = {1, 2} and B = {1, 2, 3} c) A = {1, 2, 3} and B = {2, 1, 3} d) A = {1, 2, 4} and B = {1, 2, 3} View Answer

Answer: c Explanation: Two set are equal if and only if they have the same elements. 8. The set of positive integers is _____________ a) Infinite b) Finite c) Subset d) Empty View Answer

Answer: a Explanation: The set of positive integers is not finite. 9. What is the Cardinality of the Power set of the set {0, 1, 2}? a) 8 b) 6 c) 7 d) 9 View Answer

Answer: a Explanation: Power set P ({0, 1, 2}) is the set of all subsets of {0, 1, 2}. Hence, P({0, 1, 2}) = {null, {0}, {1}, {2}, {0, 1}, {0,2}, {1, 2}, {0, 1, 2}}. 10. The members of the set S = {x | x is the square of an integer and x < 100} is ________________ a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12} b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99} d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121} View Answer

Answer: b Explanation: The set S consists of the square of an integer less than 10. Sanfoundry Global Education & Learning Series – Discrete Mathematics

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Types of Set”.

1. {x: x is an integer neither positive nor negative} is ________ a) Empty set b) Non-empty set c) Finite set d) Non- empty and Finite set View Answer

Answer: d Explanation: Set = {0} non-empty and finite set. 2. {x: x is a real number between 1 and 2} is an ________ a) Infinite set

b) Finite set c) Empty set d) None of the mentioned View Answer

Answer: a Explanation: It is an infinite set as there are infinitely many real number between any two different real numbers. 3. Write set {1, 5, 15, 25,…} in set-builder form. a) {x: either x=1 or x=5n, where n is a real number} b) {x: either x=1 or x=5n, where n is a integer} c) {x: either x=1 or x=5n, where n is an odd natural number} d) {x: x=5n, where n is a natural number} View Answer

Answer: c Explanation: Set should include 1 or an odd multiple of 5. 4. Express {x: x= n/ (n+1), n is a natural number less than 7} in roster form. a) {1⁄2, 2⁄3, 4⁄5, 6⁄7} b) {1⁄2, 2⁄3, 3⁄4, 4⁄5, 5⁄6, 6⁄7, 7⁄8} c) {1⁄2, 2⁄3, 3⁄4, 4⁄5, 5⁄6, 6⁄7} d) Infinite set View Answer

Answer: c Explanation: n/(n+1) = 1/(1+1) = 1⁄2 and n>7. 5. Number of power set of {a, b}, where a and b are distinct elements. a) 3 b) 4

c) 2 d) 5 View Answer

Answer: b Explanation: Power set of {a, b} = {∅, {a, b}, {a}, {b}}. advertisement PauseUnmute Fullscreen VDO.AI 6. Which of the following is subset of set {1, 2, 3, 4}? a) {1, 2} b) {1, 2, 3} c) {1} d) All of the mentioned View Answer

Answer: d Explanation: There are total 16 subsets. 7. A = {∅,{∅},2,{2,∅},3}, which of the following is true? a) {{∅,{∅}} ∈ A b) {2} ∈ A c) ∅ ⊂ A d) 3 ⊂ A View Answer

Answer: c Explanation: Empty set is a subset of every set. 8. Subset of the set A= { } is?

a) A b) {} c) ∅ d) All of the mentioned View Answer

Answer: d Explanation: Every set is subset of itself and Empty set is subset of each set. 9. {x: x ∈ N and x is prime} then it is ________ a) Infinite set b) Finite set c) Empty set d) Not a set View Answer

Answer: a Explanation: There is no extreme prime, number of primes is infinite. 10. Convert set {x: x is a positive prime number which divides 72} in roster form. a) {2, 3, 5} b) {2, 3, 6} c) {2, 3} d) {∅} View Answer

Answer: c Explanation: 2 and 3 are the divisors of 72 which are prime.

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Set Operations – 1”.

1. The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________ a) {1, 2, 6, 1} b) {1, 2, 5, 6} c) {1, 2, 1, 2} d) {1, 5, 6, 3} View Answer

Answer: b Explanation: The union of the sets A and B, is the set that contains those elements that are either in A or in B. 2. The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set _____________ a) {1, 2} b) {5, 6} c) {2, 5} d) {1, 6} View Answer

Answer: a Explanation: The intersection of the sets A and B, is the set containing those elements that are in both A and B. 3. Two sets are called disjoint if there _____________ is the empty set. a) Union b) Difference c) Intersection d) Complement View Answer

Answer: c Explanation: By the definition of the disjoint set. 4. Which of the following two sets are disjoint? a) {1, 3, 5} and {1, 3, 6} b) {1, 2, 3} and {1, 2, 3} c) {1, 3, 5} and {2, 3, 4} d) {1, 3, 5} and {2, 4, 6} View Answer

Answer: d Explanation: Two sets are disjoint if the intersection of two sets is the empty set. 5. The difference of {1, 2, 3} and {1, 2, 5} is the set ____________ a) {1} b) {5} c) {3} d) {2} View Answer

Answer: c Explanation: The difference of the sets A and B denoted by A-B, is the set containing those elements that are in A not in B. advertisement PauseUnmute Fullscreen VDO.AI 6. The complement of the set A is _____________ a) A – B b) U – A c) A – U

d) B – A View Answer

Answer: b Explanation: The complement of the set A is the complement of A with respect to U. 7. The bit string for the set {2, 4, 6, 8, 10} (with universal set of natural numbers less than or equal to 10) is ____________________ a) 0101010101 b) 1010101010 c) 1010010101 d) 0010010101 View Answer

Answer: a Explanation: The bit string for the set has a one bit in second, fourth, sixth, eighth, tenth positions, and a zero elsewhere. 8. Let Ai = {i, i+1, i+2, …..}. Then set {n, n+1, n+2, n+3, …..} is the _________ of the set Ai. a) Union b) Intersection c) Set Difference d) Disjoint View Answer

Answer: b Explanation: By the definition of the generalized intersection of the set. 9. The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ___________ a) 1010100000 b) 1010101101 c) 1111111100

d) 1111101010 View Answer

Answer: d Explanation: The bit string for the union is the bitwise OR of the bit strings. 10. The set difference of the set A with null set is __________ a) A b) null c) U d) B View Answer

Answer: a Explanation: The set difference of the set A by the null set denoted by A – {null} is A.

This set of Discrete Mathematics Interview Questions and Answers focuses on “Set Operations – 2”.

1. Let the set A is {1, 2, 3} and B is {2, 3, 4}. Then the number of elements in A U B is? a) 4 b) 5 c) 6 d) 7 View Answer

Answer: a Explanation: AUB is {1, 2, 3, 4}. 2. Let the set A is {1, 2, 3} and B is { 2, 3, 4}. Then number of elements in A ∩ B is? a) 1 b) 2

c) 3 d) 4 View Answer

Answer: b Explanation: A ∩ B is {2, 3}. 3. Let the set A is {1, 2, 3} and B is {2, 3, 4}. Then the set A – B is? a) {1, -4} b) {1, 2, 3} c) {1} d) {2, 3} View Answer

Answer: c Explanation: In A – B the common elements get cancelled. 4. In which of the following sets A – B is equal to B – A? a) A = {1, 2, 3}, B = {2, 3, 4} b) A = {1, 2, 3}, B = {1, 2, 3, 4} c) A = {1, 2, 3}, B = {2, 3, 1} d) A = {1, 2, 3, 4, 5, 6}, B = {2, 3, 4, 5, 1} View Answer

Answer: c Explanation: A- B= B-A = Empty set. 5. Let A be set of all prime numbers, B be the set of all even prime numbers, C be the set of all odd prime numbers, then which of the following is true? a) A ≡ B U C b) B is a singleton set. c) A ≡ C U {2}

d) All of the mentioned View Answer

Answer: d Explanation: 2 is the only even prime number. advertisement PauseUnmute Fullscreen VDO.AI 6. If A has 4 elements B has 8 elements then the minimum and maximum number of elements in A U B are ____________ a) 4, 8 b) 8, 12 c) 4, 12 d) None of the mentioned View Answer

Answer: b Explanation: Minimum would be when 4 elements are same as in 8, maximum would be when all are distinct. 7. If A is {{Φ}, {Φ, {Φ}}}, then the power set of A has how many element? a) 2 b) 4 c) 6 d) 8 View Answer

Answer: b Explanation: The set A has got 2 elements so n(P(A))=4.

8. Two sets A and B contains a and b elements respectively. If power set of A contains 16 more elements than that of B, value of ‘b’ and ‘a’ are _______ a) 4, 5 b) 6, 7 c) 2, 3 d) None of the mentioned View Answer

Answer: a Explanation: 32-16=16, hence a=5, b=4. 9. Let A be {1, 2, 3, 4}, U be set of all natural numbers, then U-A’(complement of A) is given by set. a) {1, 2, 3, 4, 5, 6, ….} b) {5, 6, 7, 8, 9, ……} c) {1, 2, 3, 4} d) All of the mentioned View Answer

Answer: c Explanation: U – A’ ≡ A. 10. Which sets are not empty? a) {x: x is a even prime greater than 3} b) {x : x is a multiple of 2 and is odd} c) {x: x is an even number and x+3 is even} d) { x: x is a prime number less than 5 and is odd} View Answer

Answer: d Explanation: Because the set is {3}.

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Sets – Venn Diagram”.

1. The shaded area of figure is best described by? discrete-mathematics-questions-answers-venn-diagram-q1 a) A ∩ B b) A U B c) A d) B View Answer

Answer: a Explanation: The region is A intersection B. 2. The shaded area of figure is best described by? discrete-mathematics-questions-answers-venn-diagram-q2 a) A‘ (Complement of A) b) A U B -B c) A ∩ B d) B View Answer

Answer: b Explanation: The region is complement of B. 3. If n(A)=20 and n(B)=30 and n(A U B) = 40 then n(A ∩ B) is? a) 20 b) 30 c) 40 d) 10 View Answer

Answer: d Explanation: n(A U B) = n(A) + n(B) – n(A ∩ B). 4. The shaded area of figure is best described by? discrete-mathematics-questions-answers-venn-diagram-q4 a) A‘ (Complement of A) b) B – (A ∩ B) – (C ∩ B) c) A ∩ C ∩ B d) B’ (Complement of B) View Answer

Answer: b Explanation: The region is difference B with A and C. 5. The relation between sets A, B, C as shown by venn diagram is __________ a) A is subset of B and B is subset of C b) C is not a subset of A and A is subset of B c) C is subset of B and B is subset of A d) None of the mentioned View Answer

Answer: c Explanation: As set C is totally inside set B, set B is totally inside set A. advertisement PauseUnmute Fullscreen VDO.AI 6. Let A: All badminton player are good sportsperson. B: All person who plays cricket are good sportsperson.

Let X denotes set of all badminton players, Y of all cricket players, Z of all good sportsperson. Then which of the following statements is correct? a) Z contains both X and Y b) Z contains X and Y is outside c) X contains Y and Z d) None of the mentioned View Answer

Answer: a Explanation: X and Y are subset of Z. 7. If n(A)=10, n(B)=30,n(C)=50 and if set A, B, C are pairwise disjoint then which of the following is correct? a) n(A U B)=0 b) n(B U C)=0 c) n(A U B U C)=90 d) All of the mentioned View Answer

Answer: d Explanation: All the statements are true based on definition. 8. In the given figure the if n(A)=20,n(U)=50,n(C)=10 and n(A∩B)=5 then n(B)=? discrete-mathematics-questions-answers-venn-diagram-q8 a) 35 b) 20 c) 30 d) 10 View Answer

Answer: a

Explanation: Here n(B)= n(U) – n(A) + n(A∩B). 9. Let the students who likes table tennis be 12, the ones who like lawn tennis 10, those who like only table tennis are 6, then number of students who likes only lawn tennis are, assuming there are total of 16 students. a) 16 b) 8 c) 4 d) 10 View Answer

Answer: c Explanation: The students who only plays lawn tennis will be a total lawn tennis player – those who play both the sports. 10. The shaded area of figure is best described by? discrete-mathematics-questions-answers-venn-diagram-q10 a) A‘ (Complement of A) b) A U B – (A ∩ B) c) A – B d) B View Answer

Answer: b Explanation: The region is complement of( A intersection B).

This set of Discrete Mathematics test focuses on “Algebraic Laws on Sets”.

1. Let C and D be two sets then which of the following statements are true?

i) C U D = D U C ii) C ∩ D = D ∩ C

a) Both of the statements b) Only i statement c) Only ii statement d) None of the statements View Answer

Answer: a Explanation: Commutative laws hold good in sets. 2. If set C is {1, 2, 3, 4} and C – D = Φ then set D can be ___________ a) {1, 2, 4, 5} b) {1, 2, 3} c) {1, 2, 3, 4, 5} d) None of the mentioned View Answer

Answer: c Explanation: C ∩ D should be equivalent to C for C – D = Φ. 3. Let C and D be two sets then C – D is equivalent to __________ a) C’ ∩ D b) C‘∩ D’ c) C ∩ D’ d) None of the mentioned View Answer

Answer: c Explanation: Set C-D will be having those elements which are in C but not in D. 4. For two sets C and D the set (C – D) ∩ D will be __________ a) C b) D

c) Φ d) None of the mentioned View Answer

Answer: c Explanation: C-D ≡ C ∩ D’, D ∩ D’ ≡ Φ. advertisement PauseUnmute Fullscreen VDO.AI 5. Which of the following statement regarding sets is false? a) A ∩ A = A b) A U A = A c) A – (B ∩ C) = (A – B) U (A –C) d) (A U B)’ = A’ U B’ View Answer

Answer: d Explanation: (A U B)’ = A’ ∩ B’. 6. Let C = {1,2,3,4} and D = {1, 2, 3, 4} then which of the following hold not true in this case? a) C – D = D – C b) C U D = C ∩ D c) C ∩ D = C – D d) C – D = Φ View Answer

Answer: c Explanation: C ∩ D = {1, 2, 3, 4} ≠ Φ. 7. If C’ U (D ∩ E’) is equivalent to __________

a) (C ∩ (D U E))’ b) (C ∩( D∩ E’))’ c) (C ∩( D’ U E))’ d) (C U ( D ∩ E’)’ View Answer

Answer: c Explanation: (C’)’≡ C, (C∩ D)’ ≡ C’ U D’. 8. Let Universal set U is {1, 2, 3, 4, 5, 6, 7, 8}, (Complement of A) A’ is {2, 5, 6, 7}, A ∩ B is {1, 3, 4} then the set B’ will surely have of which of the element? a) 8 b) 7 c) 1 d) 3 View Answer

Answer: a Explanation: The set A is {1,3,4,8} and thus surely B does not have 8 in it. Since 8 does not belong to A ∩ B. For other element like 7 we can’t be sure. 9. Let a set be A then A ∩ φ and A U φ are __________ a) φ, φ b) φ, A c) A, φ d)None of the mentioned View Answer

Answer: b Explanation: By Domination Laws on sets. 10. If in sets A, B, C, the set B ∩ C consists of 8 elements, set A ∩ B consists of 7 elements and set C ∩ A consists of 7 elements then the minimum element in set A U B U C will be?

a) 8 b) 14 c) 22 d) 15 View Answer

Answer: a Explanation: For minimum elements set B and C have 8 elements each and all of the elements are same, Also set A should have 7 elements which are already present in B and C. Thus A U B U C ≡ A ≡ B.

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Subsets”.

1. If a set contains 3 elements then the number of subsets is? a) 6 b) 3 c) 12 d) 8 View Answer

Answer: d Explanation: For elements with n elements the number of subsets are 2n. 2. The set containing all the collection of subsets is known as _________ a) Subset b) Power set c) Union set d) None of the mentioned View Answer

Answer: b

Explanation: Power set contains all the subsets as its elements. 3. If a set is empty then number of subsets will be _________ a) 1 b) 2 c) 0 d) 4 View Answer

Answer: a Explanation: The set has zero elements so 2o = 1. 4. If the number of subsets of a set are 4 then the number of elements in that sets are _________ a) 1 b) 2 c) 3 d) 4 View Answer

Answer: b Explanation: The number of elements be x then x2 = 4 thus x=2. 5. The number of subsets of a set is 5. a) True b) False View Answer

Answer: b Explanation: The number of subsets will always be a power of 2. advertisement PauseUnmute Fullscreen

VDO.AI 6. The number of subsets of a set can be odd or even. a) True b) False View Answer

Answer: a Explanation: The number of subsets will be odd in case of empty set otherwise even. 7. Let a set be A={1, 2, 3} then the number of subsets containing two elements will be _________ a) 4 b) 3 c) 5 d) 8 View Answer

Answer: b Explanation: The subsets will be {1, 2}, {2, 3}, {1, 3}. 8. Let the set be A= {a, b, c, {a,b}} then which of the following is false? a) {a, b} Є A b) a Є A c) {a} Є A d) b, c ЄA View Answer

Answer: c Explanation: Only elements belongs to a set, {a} is a subset of this set. 9. If A={1, 2, 3, 4}, then the number of the subsets of A that contain the element 2 but not 3, is? a) 16 b) 4

c) 8 d) 24 View Answer

Answer: b Explanation: The subsets would be {1, 2, 4},{1, 2}, {2, 3}, {2}. 10. Let A(1), A(2), A(3),…….., A(100) be 100 sets such that number of elements in A(i)=i+1 and A(1) is subset of A(2), A(2)is subset of A(3),….., A(99) is subset of A(100). The number of elements in union of the all the sets are: n(A(1) U A(2) U A(3) …..U A(100)). a) 99 b) 100 c) 101 d) 102 View Answer

Answer: c Explanation: Since all sets are subsets of A(100) therefore in union only elements of A(100)will come. A(100) contains 101 elements.

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Functions”.

1. A function is said to be ______________ if and only if f(a) = f(b) implies that a = b for all a and b in the domain of f. a) One-to-many b) One-to-one c) Many-to-many d) Many-to-one View Answer

Answer: b

Explanation: A function is one-to-one if and only if f(a)≠f(b) whenever a≠b. 2. The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False? a) True b) False View Answer

Answer: a Explanation: For every integer “y” there is an integer “x ” such that f(x) = y. 3. The value of ⌊1/2.⌊5/2⌋ ⌋ is ______________ a) 1 b) 2 c) 3 d) 0.5 View Answer

Answer: a Explanation: The value of ⌊5/2⌋ is 2 so, the value of ⌊1/2.2⌋ is 1. 4. Which of the following function f: Z X Z → Z is not onto? a) f(a, b) = a + b b) f(a, b) = a c) f(a, b) = |b| d) f(a, b) = a – b View Answer

Answer: c Explanation: The function is not onto as f(a)≠b. 5. The domain of the function that assign to each pair of integers the maximum of these two integers is ___________ a) N
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