Discrete Mathematics GATE Questions

Practising previous years’ GATE Questions papers are the most widely used way to prepare for the GATE Exam. Candidates can practise, analyse and learn concepts while solving them. It helps students strengthen their time management skills. We have attempted to compile, here in this article, a collection of GATE Questions on Discrete Mathematics.

Candidates are urged to practise these Discrete Mathematics GATE previous years’ questions to get the best results. Discrete Mathematics is an important topic in the GATE question papers, and solving these questions will help the candidates to prepare more proficiently for the CSE GATE exams. Therefore, candidates can find the GATE Questions for Discrete Mathematics in this article to solve and practise well before the exams. They can also refer to these GATE previous year question papers and start preparing for the exams.

GATE Questions on Discrete Mathematics

1. Let R be the set of all binary relations on the set {1,2,3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is ____.

(GATE CSE 2020)

1. 0.125
2. 0.150
3. 0.175
4. 0.200

Answer (a)

2. Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is _____.

(GATE CSE 2019)

1. 7
2. 9
3. 1
4. 0

Answer (a)

3. Let 𝑅 be the relation on the set of positive integers such that aR if and only if 𝑎 and 𝑏 are distinct and have a common divisor other than 1. Which one of the following statements about 𝑅 is true?

(GATE CSE 2015 Set 2)

1. R is symmetric and reflexive but not transitive
2. R is reflexive but not symmetric and not transitive
3. R is transitive but not reflexive and not symmetric
4. R is symmetric but not reflexive and not symmetric

Answer (d)

4. consider the binary relation R={(x,y),(x,z),(z,x),(z,y)} on the set {x,y,z}. Which one of the following is TRUE?

(GATE CSE 2009)

1. R is symmetric but NOT antisymmetric
2. R is NOT symmetric but antisymmetric
3. R is both symmetric and antisymmetric
4. R is neither symmetric nor antisymmetric

Answer (d)

5. Which one of the following is NOT necessarily a property of the Group?

(GATE CSE 2009)

1. Commutativity
2. Associativity
3. Existence of inverse for every element
4. Existence of identity

Answer (a)

6. Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S is _______.

(GATE CSE 2009)

1. n and n
2. n² and n
3. n² and 0
4. n and 1

Answer (b)

7. A relation R is defined on ordered pairs of integers as follows: (x,y)R(u,v) if x<u and y>v. Then R is ______.

(GATE CSE 2006)

1. Neither a Partial Order nor an Equivalence Relation
2. A Partial Order but not a Total Order
3. A Total Order
4. An Equivalence Relation

Answer (a)

8. The set {1,2,3,5,7,8,9} under multiplication modulo 10 is not a group. Given below are four plausible reasons.

Which one of them is false?

(GATE CSE 2006)

1. It is not closed
2. 2 does not have an inverse
3. 3 does not have an inverse
4. 8 does not have an inverse

Answer (c)

9. The set {1,2,4,7,8,11,13,14} is a group under multiplication modulo 15. The inverse of 4 and 7 are respectively:

(GATE CSE 2005)

1. 3 and 13
2. 2 and 11
3. 4 and 13
4. 8 and 14

Answer (c)

10. Let A, B and C be non-empty sets and let X=(A−B)−C and Y=(A−C)−(B−C). Which one of the following is TRUE?

(GATE CSE 2005)

1. X = Y
2. \(\begin{array}{l}X \subset Y\end{array} \)
3. \(\begin{array}{l}Y \subset X\end{array} \)
4. None of the above

Answer (a)

11. Consider the following relations:

R1(a,b) iff (a+b) is even over the set of integers

R2 (a,b) iff (a+b) is odd over the set of integers

R3 (a,b) iff a.b>0 over the set of non-zero rational numbers

R4 (a,b) iff |a−b|≤2 over the set of natural numbers

(GATE CSE 2001)

1. R₁ and R₂ are equivalence relations; R₃ and R₄ are not
2. R₁ and R₃ are equivalence relations; R₂ and R₄ are not
3. R₁ and R₄ are equivalence relations; R₂ and R₃ are not
4. R₁, R₂, R₃, and R₄ are all equivalence relations

Answer (b)

12. The number of functions from an m element set to an n element set is ________.

(GATE CSE 1998)

1. m + n
2. mⁿ
3. n^m
4. m * n

Answer (c)

13. Suppose A is a finite set with n elements. The number of elements in the Largest equivalence relation of A is ________.

(GATE CSE 1998)

1. n
2. n²
3. 1
4. n + 1

Answer (b)

14. The number of equivalence relations on the set {1,2,3,4} is _______.

(GATE CSE 1997)

1. 15
2. 16
3. 24
4. 4

Answer (a)

15. Which of the following statements is false?

(GATE CSE 1996)

1. The set of rational numbers is an abelian group under addition
2. The set of integers is an abelian group under addition
3. The set of rational numbers from an abelian group under multiplication
4. The set of real numbers excluding zero is an abelian group under multiplication

Answer (c)