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Core topics - Intro to Discrete Math


Trees: -

In graph theory, trees are the graphs which are undirected and no two vertices can be connected by more than one path. It is used to solve various complex real-life problems.

 

Sequence: -

Mathematically, sequence is  f:N→A (a function f from natural number to a set A). In other words, sequence is a pattern between elements of a set in an ordered way. For example, 1, 3, 32, 33……… 

 

Series: -

Summation of sequence is known as series. It is denoted by the symbol sigma. Arithmetic series, geometric series, and Fibonacci series are some examples for that.

 
Boolean Algebra: -

Boolean algebra uses binary variables and deals with operation on logical statements, that is how a logical statement can validate itself using a truth table. 

 

Sets: - 

Sets can be defined as a “defined collection of any particular thing” which means that collection should be the same to everyone. For example a collection of top 10 writers is not an asset but a collection of books of Shakespeare is a set.


Graph theory: -

Graph theory is all about the set of points called vertices or nodes connected by lines known as paths. It is widely used to solve the complex strategic problems.


Group Theory: -

A mathematical operation with a set follows some properties, then that set is called a group under that operation. Those properties are Closure, Associative, Identity element, and existence of Inverse.

 

Permutation and Combination: -

This concept in math is used to find the number of ways to arrange or select certain things. For example, find the number of ways to select 3 boys out of a group of 7 boys. 


Mathematical logic: -

In this, we have some set of statements to check whether they are logical, correct or not. For that we have some set of rules in order to check if that statement makes some sense or not according to those rules.

 

Relation and function: - 

Relation and function are the subset of the cartesian product of two sets, in relation we have some common property followed by the elements and function are a special type of relation in which every element has a unique image.

 

Counting Theory: -  

When we have to find the total number of ways in which a particular scenario can be done we have to count each and every possibility in such cases counting theory comes in handy. Permutation and combination are the two methods which help in counting those possibilities.
 

Sample Discrete Math Practice Problems:


Q1. Are the statements (P ∨ Q) → R and (P → R) ∨ (Q → R) logically equivalent?

Sol. 

P

Q

R

(P ∨ Q) → R

(P → R) ∨ (Q → R)

T

T

T

T

T

T

T

F

F

F

T

F

T

T

T

T

F

F

F

T

F

T

T

T

T

F

T

F

F

T

F

F

T

T

T

F

F

F

T

T

the statements are not logically equivalent.

Q2. Is it possible for a planar graph to have 6 vertices, 10 edges and 5 faces? Explain

Sol. No. 

A (connected) planar graph must satisfy Euler's formula                   

             V – E + F = 2

V – E + F = 2

Here  V – E + F = 6 – 10 + 5 = 1

So, it is not possible 

 


Discrete Math Sample Questions:

Question 1: Recurrence relation is formed of:


(a) Rules to generate the next term in the sequence

(b) Current Value

(c) Starting Value

(d) Both (a) and (b)


Answer: (c)

Explanation: The recurrence relation is made of starting value.

 

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Question 2: Find the recursive formula for the sequence 3,6,12,24,48,96…..


Find the recursive formula for the sequence


Answer: (a)

Explanation: Use the recursive formula.

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Question 3: An algebraic structure ____________is called a semigroup.


An algebraic structure


Answer: (a)

Explanation: The ones which satisfy closure property and associative property are called as semi-group.

 

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Question 4: {1,-1,I,-1} is ______________under multiplication.

 

(a) Semi Group

(b) Cyclic Group

(c) Abelian Group

(d) All of the above


Answer: (d)

Explanation: Abelian Group

 

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Question 5: Let ( Z, *) is a  group with a*b = a+b-2 then inverse of a is:

 

inverse


Answer: (a)

Explanation: discreet-math answer

 

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Question 6:  For semigroup homomorphism the condition should be


semigroup homomorphism the condition should be


Answer: (d)

Explanation: Isomorphism is the condition for …….

 

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Question 7: Let H and K be any two subgroup of a group G. H???? Ụ K is a subgroup on_________.  


Let H and K be any two subgroup of a group G


Answer: (b)

Explanation: H???? Ụ K is a subgroup if one is contained in other.

 

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Question 8: In the set of integers with operation * defined by a*b = a+b-ab, the value of 3*(4*5) is:

 

(a) 25

(b) 15

(c) 10

(d) 5


Answer: (a)

Explanation: 3*(4*5)  = 3*(4+5-20) = 3*(-11) = 3 + (-11) -3(-11).....

 

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Question 9: If a, b are positive integers, define a*b = a where ab= a(modulo 7), with this * operation, then inverse of 3 in group G = { 1,2,3,4,5,6} is___________.

 

(a) 3

(b) 1

(c) 5

(d) 4


Answer: (c)

Explanation: 3 * 1 = 3

3 * 2 = 6....

 

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Question 10: (Z*) is a group in which x*y = x+y -2, find the inverse of x:


is a group in which x*y = x+y -2, find the inverse of x


Answer: (a)

Explanation: discreet-math explanation

 

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Study Discrete Mathematics Online at TutorEye

Discrete mathematics is the branch of mathematics that deals with objects that can assume only distinct, separated values such as integers. This branch of mathematics gained popularity only in the last few decades due to the growth and dependency of the world on computers and information technology. Discrete mathematics emerged as a separate area of study beginning late 1960s at the upper graduate student’s level.


The introduction to discrete mathematics in primary and secondary schools (K-12) in the United States was encouraged and facilitated by the recommendations of the National Council of Teachers of Mathematics in the curriculum and evaluation standards of school mathematics 1989). 


Some of the common and everyday applications of discrete mathematics include computer run software that uses binary math. Network connections are discrete structures, online maps such as Google & Apple use discrete math to calculate the fastest routes & times. Railway planning also uses discrete math. 


Discrete math was usually a course opted by the students of computer science. Therefore, it is also known as “math for computer science.” It is also related to the fields of cryptology, automated theorem proving, programming language, and software development and plays a significant role in big data analytics. 


So in the 21st century, where understanding of computer codes and programming languages is a necessity for everyone, studying and understanding concepts of Discrete Mathematics is a must. 


If you are a parent wanting to help your kid with discrete mathematics homework or get ready for Discrete Math Final Exam, don’t hesitate to seek assistance and guidance from our pool of expert discrete math tutors.  


In fact, our team of experts at TutorEye recommend that every student starting from the 6th grade should invest time and effort into studying fundamentals of discrete math, especially combinatorics, graph theory, discrete geometry, number theory, and discrete probability. 


Many students find Discrete Math to be a hard subject because those students aren’t able to get the right guidance with the subject early on and hence, due to weak foundation, they start to fear the concepts. 


Don’t worry if your child is fearing homework assignments of discrete math. You will get help from the finest tutors who will break down complicated concepts and topics for your child and help them form a strong foundation.


Many high school and college level students may even look for simplification calculators, apps, and pdfs online to get help with discrete math homework assignments. But in this whole they just get answers to the homework problems without understanding the logic applied to solve the discrete math problems. By taking our written help service, you will be provided a detailed walkthrough so that you can gain insight on problems and improve your confidence at the same time.


Our tutors provide step-by-step solutions to help you figure the working behind assigned questions. With the help of these detailed walkthroughs, one can gain conceptual clarity over tough topics. 


If you are wondering what’s the difference between recursion and induction, take help from our tutors right away. Go over your homework questions and chat with our tutors to seek written solutions to help you map out your problems.


The following topics are covered in Discrete Math:
 

  • Set theory and notation
  • Algorithms
  • Computing modules, Basic number theory, and integer definitions
  • Combinatorics
  • Algebraic Structures
  • Topology
  • Discrete analysis or discrete calculus
  • Game theory
  • Utility Theory
  • Decision Theory
  • Social Choice Theory
  • Operations Research
  • Number Theory
  • Logic
  • Information Theory
  • Representation of Integers

 

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Frequently Asked Questions about Statistics Homework Help:

Is discrete math difficult?

Discrete Math is not difficult but requires practice on the part of the student. If you are finding this subject difficult, you must :

  • Analyze each topic
  • Focus on problem-solving aspects
  • Think through the given problems
  • Hone your logical thinking skills
  • Come up with solutions
  • Work through proof

Besides, you can always get discrete math help at TutorEye. Our experts do not abide by the philosophy that either “you get it or you don’t get it”. It’s simply a matter of putting in sufficient practice and you will no longer find the subject difficult.

 

How does online discrete math tutoring work?

Discrete Math tutoring works well for most of the students as it is quite simple and efficient. Here you get a chance to study at your pace and solve as many problems as you want. Besides you can go over the solutions and look at the different approaches that can be used to solve a problem that may not be possible in a classroom situation.
 
Also, you can choose to get discrete math homework help from a qualified professional depending on your needs. By getting step-wise explanations you can easily understand how to work through proofs.
 
Whether it is logical equivalence, o-notation, the difference between induction and recursion- you can get notes or detailed solutions from our top academicians anytime you want.

 

How to learn discrete mathematics?

The best way to learn discrete mathematics is to solve as many questions as you can. Start early by devoting time to graph theory and combinatorics. Here is what you need to do:

  • Get into the habit of working through logic and proof
  • Avoid common logical errors
  • Verify solutions by carrying out mathematical induction
  • Attend classes and lectures
  • Start solving combinatorial problems early on
  • Pay close attention to notation
  • Look at the exact phrasing of each question to answer correctly

Apart from this, you need to be under the supervision of qualified professionals like us. It is important to get discrete math help on time to resolve doubts as and when they arise. Therefore, you need to bank on our proficient experts who are adept at handling all student-related problems and make learning fun.

 

What is a bijection in discrete math?

If there is one to one correspondence between the elements of two sets under a function then we say that the function is bijective.

 

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