Table of Contents

**MTH202: Discrete Mathematics**

Discrete mathematics is a mathematical unit that deals with objects that can only take different, different values. Therefore, the term “discrete mathematics” is used in contrast to “continuous mathematics,” which is a branch of mathematics that deals with fluctuations. Although different objects can often be identified by whole numbers, continuous objects require real numbers. MTH202 Handouts pdf

#### MTH202 Handouts pdf

**Course Category: Mathematics **MTH202 Handouts pdf

**Course Outline**

Logic, Sets & Operations on sets, Relations & Their Properties, Functions, Sequences & Series, Recurrence Relations, Mathematical Induction, Loop Invariants, Loop Invariants, Combinatorics, Probability, Graphs and Trees. MTH202 Handouts pdf

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### MTH202 HANDOUTS

**MTH202: Discrete Mathematics**

**Fundamentals of Mathematical Logic**

Logic is commonly known as the science of thought. The emphasis here will be on logic as a working tool. We will develop some of the metaphorical techniques needed in the computer concept. Some of the reasons for learning logic are the following:

At the computer level, the formation of ‘logic’ circles for guidance is made much easier by the use of symbolic concepts.

At the software level, figurative knowledge is useful for programming.

** Rules of Inferential Logic **

The main concern of the concept is how the truth of some proposals is linked to the truth of another. Thus, we will usually consider a group of related suggestions. An argument is a set of two or more suggestions that are related to each other in such a way that all but one of them (properties) should provide the remaining support (conclusion). The transition from place to place is an assumption on which the argument is based.

**For example**

”The star is made up of milk, and red strawberries. My dog has a flea. ” do not quarrel. Solution. Of course, the truth or falsehood of each proposal has no bearing on the other.

#### Propositions and Quantifiers

Statements such as “x> 3” are often found in mathematical assumptions and computer programs. These statements are not suggestions when the variables are not specified. However, one can generate suggestions on such statements. An adverb is a phrase that involves one or more variables defined in a particular domain, called a speech domain.

Substituting a certain amount of variance produces a suggestion that may be true or false. For example, P (n): n is a pronoun for natural numbers. Note that P (1) is false, and P (2) is true. In the expression P (x), x is called a free variable. As x varies the true value of P (x) also varies. The true value set of the predicate P (x) is called the true set and will be defined as TP.

#### Digital Logic Design

In this section, we discuss the logic of digital circuits which are considered to be the basic components of many digital systems, such as computers, electric phones, traffic light controls, etc. The purpose of digital programs is to manipulate a variety of represented information. at visible values such as voltage and current. The smallest representation unit is one bit, shorter by binary digit.

Since the electronic switch has two visible modes, namely high voltage and low voltage we put a bit at high voltage and 0 bit at low voltage. The sensible gateway is the smallest processing unit in the digital system. It takes one or a few bits as input and produces slowly as output.