Table of Contents
Discrete Mathematics GATE Questions Types
Discrete Mathematics is an important subject of computer science branch for GATE Exam perspective. Questions from discrete mathematics are always asked in GATE exam. Discrete mathematics gate questions consist approx. 5 to 8 marks out of 100.
In this tutorial we have discussed variety of discrete mathematics questions. These questions will be helpful for computer science students to understands the discrete mathematics concepts. If a computer science student or students appearing in GATE (CS)or UGC NET (CS) exam will practice these discrete mathematics gate questions type then he or she will be able to solve the discrete mathematics gate questions easily.
Table of Content
- Discrete Mathematics syllabus for gate cse
- Definition types discrete mathematics questions
- Discrete mathematics gate questions type
- Conclusion and Summary
Discrete Mathematics Syllabus for GATE CSE
This is important and advisable for GATE CSE 2022 Aspirant to know the Discrete mathematics syllabus for gate cse before starting to solve the discrete mathematics gate questions. Here in this section we have discussed the Discrete mathematics syllabus for gate cse.
Discrete mathematics syllabus for gate cse is given below –
- Propositional and first-order logic.
- Sets, relations, functions, partial orders and lattices.
- Groups
- Graphs: connectivity, matching, coloring.
- Combinatorics: counting, recurrence relations, generating functions.
Definition Type DSTL Questions
Definition types dstl questions can be asked in the viva voce or in university exam. These questions are specially prepared for B.Tech(CSE), BCA, MCA students who are studying discrete mathematics subject. These questions are given below –
Q1.What Is Discrete Mathematics?
Q2. What Are The Categories Of Mathematics?
Q3. What Is Sets In Discrete Mathematics?
Q 4. In How Many Ways Represent A Set?
Q 5. Explain Some Important Sets?
Q6. What Is Cardinality Of A Set?
Q 7. What Are The Types Of Sets?
Q 8. What Is Set Operations?
Q 9. What Is Power Set?
Q 10. What Is Partitioning Of A Set?
Q11. What Is Bell Numbers?
Q 12. What Is Discrete Mathematics Relations?
Q13. What Is Discrete Mathematics Functions?
Q14. What Is Composition Of Functions?
Q15. What Is Propositional Logic?
Q 16. What Are Connectives?
Q17. What Are Tautologies?
Q 18. What Are Contradictions?
Q 19. What Is Contingency?
Q 20. What Are Propositional Equivalences?
Q 21. What Is Duality Principle?
Q 22. What Are The Types Of Normal Forms?
Q23. What Is Predicate Logic?
Discrete Mathematics GATE Questions Types
Discrete mathematics gate questions type are generally multiple choice questions. Questions aconsist8ng one marks and two marks questions are generally asked in GATE Exam.
Q 24 Which of the following are well-defined sets?
(a) All the colors in the rainbow.
(b)Set of points that belong to a straight line.
(c) All the honest members in the family.
(d) All the consonants of the English alphabet.
(e) All the tall boys of the school.
(f) All the efficient doctors of the hospital.
(g) All the hardworking teachers in a school.
(h) All the prime numbers less than 100.
(i) All the letters in the word GEOMETRY.
Q25. The union of the sets {1, 2, 5} and {1, 2, 6} is that the set _______________
a) {1, 2, 6, 1}
b) {1, 2, 5, 6}
c) {1, 2, 1, 2}
d) {1, 5, 6, 3}
Q26. 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}
Q27. Two sets are called disjoint if there are a selection is that the empty set.
a) Union
b) Difference
c) Intersection
d) Complement
Q28. 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}
Q29. The difference of {1, 2, 3} and {1, 2, 5} is the set ____________
a) {1}
b) {5}
c) {3}
d) {2}
Q30. The complement of the set A is _____________
a) A – B
b) U – A
c) A – U
d) B – A
Q31. 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
Q32. 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
Q33. Two sets has the bit strings 1111100000 and 1010101010 respectively. What is the union of the set ___________
a) 1010100000
b) 1010101101
c) 1111111100
d) 1111101010
Q34. The set difference of the set A with null set is __________
a) A
b) null
c) U
d) B
Q35. Let the set A is {1, 2, 3} and B is {2, 3, 4}. How many elements are there in A U B is
a) 4
b) 5
c) 6
d) 7
Q36. Let the set A is {1, 2, 3} and B is { 2, 3, 4}. How many elements are there in A ∩ B is
a) 1
b) 2
c) 3
d) 4
Q37. 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}
Q38. 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}
Q39. A is a set of all prime numbers and B is the set of all even prime numbers and C is the set of all odd prime numbers, then find the correct option.
a) A ≡ B U C
b) B is a singleton set.
c) A ≡ C U {2}
d) All of the mentioned
Q40. If A has 4 elements B has 8 elements then the minimum and maximum number of elements in A U B are respectively
a) 4, 8
b) 8, 12
c) 4, 12
d) None of the mentioned
Q41. If A is {{Φ}, {Φ, {Φ}}, then the power set of A has how many element?
a) 2
b) 4
c) 6
d) 8
Q42. 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 respectively
a) 4, 5
b) 6, 7
c) 2, 3
d) None of the mentioned
Q43. 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
Q44. Which sets are not empty?
a) {x: x is even prime greater than 3}
b) {x : x is a multiple of 2}
c) {x: x is an even number and x+3 is even}
d) { x: x may be a prime but 5 and is odd}
Q45. A function is claimed to remember if and as long as f(a) = f(b) implies that a = b for all a and b within the domain of f.
a) One-to-many
b) One-to-one
c) Many-to-many
d) Many-to-one
Q46. The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False?
a) True
b) False
Q47. Consider the set A = {2, 7, 14, 28, 56, 84} and the relation a ≤ b if and only if a divides b. Give the Hasse diagram for the poset (A,≤).
Q48. Which of the subsequent function f: Z X Z → Z isn’t onto?
a) f(a, b) = a + b
b) f(a, b) = a
c) f(a, b) = |b|
d) f(a, b) = a – b
Q49. The domain of the function that assign to every pair of integers the utmost of those two integers is an excellent
a) N
b) Z
c) Z +
d) Z+ X Z+
Q50.Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is an outstanding
a) 6x + 9
b) 6x + 7
c) 6x + 6
d) 6x + 8
Q51. __________ bytes are required to encode 2000 bits of knowledge .
a) 1
b) 2
c) 3
d) 8
Q52. The inverse of function f(x) = x3 + 2 is ____________
a) f -1 (y) = (y – 2) 1/2
b) f -1 (y) = (y – 2) 1/3
c) f -1 (y) = (y) 1/3
d) f -1 (y) = (y – 2)
Q53. The function f(x) = x3 is bijection from R to R. Is it True or False?
a) True
b) False
Q54. For an inverse to exist it’s necessary that a function should be :
a) injection
b) bijection
c) surjection
d) none of the mentioned
Q55. If f(x) = y then f -1(y) is equal to :
a) y
b) x
c) x2
d) none of the mentioned
Q56. A function f(x) is defined from A to B then f -1 is defined :
a) from A to B
b) from B to A
c) depends on the inverse of function
d) none of the mentioned
Q57. If f is a function defined from R to R , is given by f(x) = 3x – 5 then f –1(x) is given by:
a) 1/(3x-5)
b) (x+5)/3
c) doesn’t exist since it’s not a bijection
d) none of the mentioned
Q58. State whether the given statement is true or false
For some bijective function inverse of that function isn’t bijective.
a) True
b) False
Q59. State whether the given statement is true or false
f(x) may be a bijection than f -1(x) may be a reflection of f(x) around y = x.
a) True
b) False
Q60. f is a function defined from R to R , is given by f(x) = x2 then f –1(x) is given by:
a) 1/(3x-5)
b) (x+5)/3
c) doesn’t exist since it’s not a bijection
d) none of the mentioned.
Q61. Represent the following statement in predicate calculus: Everybody respects all the selfless leaders
Q62. The solution to f(x) = f -1(x) are :
a) no solutions in any case
b) same as solution to f(x) = x
c) infinite number of solution for every case
d) none of the mentioned
Q63. State True or False.
Let f(x) = x then number of solution to f(x) = f -1(x) is zero.
a) True
b) False
Q64. compound proposition that is always ___________ is called a tautology.
a) True
b) False
Q65. A compound proposition that is always ___________ is called a contradiction.
a) True
b) False
Q66. If A is any statement, then which of the subsequent may be a tautology?
a) A ∧ F
b) A ∨ F
c) A ∨ ¬A
d) A ∧ T
Q67. If A is any statement, then which of the subsequent isn’t a contradiction?
a) A ∨ ¬A
b) A ∨ F
c) A ∧ F
d) None of mentioned.
Q68. A compound proposition that is neither a tautology nor a contradiction is called a ___________
a) Contingency
b) Equivalence
c) Condition
d) Inference
Q69. ¬ (A ∨ q) ∧ (A ∧ q) is a ___________
a) Tautology
b) Contradiction
c) Contingency
d) None of the mentioned
Q70. (A ∨ ¬A) ∨ (q ∨ T) may be a __________
a) Tautology
b) Contradiction
c) Contingency
d) None of the mentioned
Q71. A ∧ ¬(A ∨ (A ∧ T)) is always __________
a) True
b) False
Q72. (A ∨ F) ∨ (A ∨ T) is always _________
a) True
b) False
Total Words: 795
Q73. A → (A ∨ q) is a __________
a) Tautology
b) Contradiction
c) Contingency
d) None of the mentioned
Q74. Let P (x) denote the statement “x >7.” Which of these have truth value true?
a) P (0)
b) P (4)
c) P (6)
d) P (9)
Q75. How many edges are there in an undirected graph with two vertices of degree 7, four vertices of degree 5, and the remaining four vertices of degree is 6?
Q76. Determine the truth value of ∀n(n + 1 > n) if the domain consists of all real numbers.
a) True
b) False
Q77. Let P(x) denote the statement “x = x + 7.” What is the truth value of the quantification ∃xP(x), where the domain consists of all real numbers?
a) True
b) False
Q78. Let R (x) denote the statement “x > 2.” What is the truth value of the quantification ∃xR(x), having domain as real numbers?
a) True
b) False
Q79. The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.
a) ∃x(C(x) ∧ F (x))
b) ∀x(C(x) ∧ F (x))
c) ∃x(C(x) → F (x))
d) ∀x(C(x) → F (x))
Q80. The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.
a) ∀x (F (x) → P (x))
b) ∀x (F (x) ∧ P (x))
c) ∃x (F (x) ∧ P (x))
d) ∃x (F (x) → P (x))
Q81. ”Everyone wants to find out cosmology.” This argument could also be true that domains?
a) All students in your cosmology class
b) All the cosmology learning students within the world
c) Both of the mentioned
d) None of the mentioned
Q82. Let domain of m includes all students , P (m) be the statement “m spends more than 2 hours in playing polo”. Express ∀m ¬P (m) quantification in English.
a) A student is there who spends quite 2 hours in playing polo
b) there’s a student who doesn’t spend quite 2 hours in playing polo
c) All students spends quite 2 hours in playing polo
d) No student spends more than 2 hours in playing polo
Q83. Determine the reality value of statement ∃n (4n = 3n) if the domain consists of all integers.
a) True
b) False
Q84. Which of the following statement is a proposition?
a) Get me a glass of milkshake
b) God bless you!
c) What is the time now?
d) The only odd prime number is 2
Q85.Which of the following option is true?
a) If the Sun is a planet, elephants will fly
b) 3 +2 = 8 if 5-2 = 7
c) 1 > 3 and 3 is a positive integer
d) -2 > 3 or 3 is a negative integer
Q86. What is the value of x after this statement, assuming initial value of x is 5?
‘If x equals to at least one then x=x+2 else x=0’.
a) 1
b) 3
c) 0
d) 2
Q87. Let P: I am in Bangalore. , Q: I love cricket. ; then q -> p(q implies p) is:
a) If I love cricket then I am in Bangalore
b) If I am in Bangalore then I love cricket
c) I am not in Bangalore
d) I love cricket
Q88. Let P:If Sahil bowls, Saurabh hits a century. ,Q: If Raju bowls , Sahil gets out on first ball. Now if P is true and Q is fake then which of the subsequent are often true?
a) Raju bowled and Sahil got out on first ball
b) Raju did not bowled
c) Sahil bowled and Saurabh hits a century
d) Sahil bowled and Saurabh got out
Q89. The truth value of given statement is
‘If 9 is prime then 3 is even’.
a) False
b) True
Q90 Let P: I am in Delhi. , Q: Delhi is clean. ; then q ^ p(q and p) is:
a) Delhi is clean and I am in Delhi
b) Delhi is not clean or I am in Delhi
c) I am in Delhi and Delhi is not clean
d) Delhi is clean but I am in Mumbai
Q91. Let P: this is often an excellent website, Q: you ought to not come here. Then ‘This may be a great website and you ought to come here.’ is best represented by:
a) ~P V ~Q
b) P ∧ ~Q
c) P V Q
d) P ∧ Q
Q92. Let P: We should be honest., Q: We should be dedicated .,R: We should be overconfident.
Then ‘We should be honest or dedicated but not overconfident.’ is best represented by:
a) ~P V ~Q V R
b) P ∧ ~Q ∧ R
c) P V Q ∧ R
d) P V Q ∧ ~R
Q93. In a survey of 85 people it is found that 31 like to drink milk, 43 like coffee and 39 like tea. Also 13 like both milk and tea, 15 like milk and occasional , 20 like tea and occasional and 12 like none of the three drinks. Find the number of people who like all the three drinks. Display the answer using a Venn diagram.
Q94. If B is a Boolean Algebra, then which of the following is true
(A)B is a finite but not complemented lattice.
(B)B is a finite, complemented and distributive lattice.
(C)B may be a finite, distributive but not complemented lattice.
(D)B is not distributive lattice
Q95. Define a complete lattice and give one example
Q96. The converse of a statement is: If a steel rod is stretched, then it has been heated. Write the inverse of the statement.
Q97. Is (P∧ Q)∧ ~(P∨ Q) a tautology or a fallacy?
Q98. In how many ways 5 children out of a class of 20 line up for a picture.
Q99. If P and Q stands for the statement
P : It is hot
Q : It is humid, then what does the following mean? P ∧ ( ~ Q) :
Q100. In a survey of 85 people it is found that 31 like to drink milk, 43 like coffee and 39 like tea. Also 13 like both milk and tea, 15 like milk and occasional , 20 like tea and occasional and 12 like none of the three drinks. Find the amount of individuals who like all the three drinks. Display the answer using a Venn diagram.
Conclusion and Summary
In this tutorial discrete mathematics gate questions types are discussed along with discrete mathematics syllabus for gate cse. These questions are just for practice. In next tutorial we will also discussed previous year GATE questions of Discrete Mathematics with proper solution and explanation.
I kindly request to students please practice these questions if you have nay problem then ask in comment section. Students can also comment the answer of the questions.
