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Discrete Mathematics is an important subject in the field of computer science. It is a branch of mathematics that deals with discrete objects and structures. One of the popular exams that test your knowledge in Discrete Mathematics among other subjects is the GATE exam. In this post, we will go through some Discrete Mathematics GATE questions types and also learn about the solutions to those questions.

Discrete Mathematics GATE Questions Types

Here are some popular Discrete Mathematics GATE questions types:

Set Theory

Set Theory is the study of sets, which are collections of objects. It is one of the most important areas of Discrete Mathematics. In the GATE exam, a lot of questions are asked from Set Theory. You will be tested on the concepts of sets, types of sets, operations on sets, and Venn diagrams.

Relations and Functions

Relations and Functions are another important area of Discrete Mathematics. A relation is a set of ordered pairs while a function is a relation where each input has a unique output. In the GATE exam, you will be tested on the properties of relations, equivalence relations, partial orders, and functions.

Graph Theory

Graph Theory is the study of graphs, which are structures that consist of vertices and edges. In the GATE exam, a lot of questions are asked from Graph Theory. You will be tested on the types of graphs, Euler and Hamiltonian paths and circuits, shortest paths, and matching.

Now that we have an idea of the types of questions that can be asked in the GATE exam, let's look at some solutions.

Solutions to Discrete Mathematics GATE Questions

Here are some solutions to the popular Discrete Mathematics GATE questions types we just discussed:

Set Theory

Example: Let A = a, b, c, B = b, c, d, and C = c, d, e. Determine:

1. A ∩ B
2. A ∪ C
3. A − B
4. B − A

Solution:

1. A ∩ B = b, c
2. A ∪ C = a, b, c, d, e
3. A − B = a
4. B − A = d

Relations and Functions

Example: Let R be a relation on the set of real numbers defined by xRy if and only if |x-y|≤3. Show that R is an equivalence relation.

Solution:

To show that R is an equivalence relation, we need to show that it satisfies the following three properties:

1. Reflexive
2. Symmetric
3. Transitive

To show that R is reflexive, we need to show that xRx for all x ∈ R. Since |x-x| = 0 ≤ 3, this is true.

To show that R is symmetric, we need to show that if xRy, then yRx for all x, y ∈ R. Since |x-y| = |y-x|, this is true.

To show that R is transitive, we need to show that if xRy and yRz, then xRz for all x, y, z ∈ R. Since |x-z| ≤ |x-y| + |y-z| ≤ 6, this is true.

Therefore, R is an equivalence relation.

Graph Theory

Example: Let G be a graph with 6 vertices and 10 edges. What is the degree sum of G?

Solution:

The degree sum of a graph is the sum of the degrees of all its vertices. The degree of a vertex is the number of edges that are incident to it. Since there are 10 edges in G, the sum of the degrees of all vertices is 2*10 = 20. Therefore, the degree sum of G is 20.

These were just some examples of the types of questions and solutions that you can expect in the GATE exam for Discrete Mathematics. It is important to have a good understanding of the basics and practice as many questions as possible to score well in the exam.

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