Venn Diagram, Universal Sets, Subsets, and Power Sets

In the previous article, you learned about the basic type of sets and its notations. In this article, I am going to discuss about Venn diagram, and some other types of sets. These sets are different from what I have discussed in my previous post, which was about equal sets, equivalent set and empty sets … Read more

Types of Basic Sets

In the previous article, you learnt about set notations – the roster notation and the set builder notation. In this article, I will discuss about the types of sets available. This is part 1 where we see basic types of sets and in part 2, I will discuss some derived types. Set Types The sets … Read more

Introduction To Sets

In this article, I will introduce you to sets and its notations. There are many definitions for sets. But no one single definition is acceptable. So, I will start with a simple informal definition of a set. “A set is group of objects with some properties and sometimes the object from same group does not … Read more

Logical Equivalence – Domination Laws

In the previous article, you learnt about Identity law which is an equivalence. Similarly, the domination law are another equivalence that you are going to learn in this article. Also, this equivalence need proof which is the main purpose of this document. The prove is in the form of truth table for domination laws. What … Read more

Logical Equivalence – Identity Law

Earlier you learned about the logical equivalence and how two or more compound prepositions makes a tautology and prove their equivalence. There are many well-known , so first one is identity law. We call it law because the same logic is applied in which is another branch of mathematics, that studies and understand logic in … Read more

List of Logical Equivalences and Truth Tables

In this article, you will know the list of known logical equivalences and their corresponding truth table as a proof of them being a tautology. To understand more in-depth analysis of each of the identities, you can watch my YouTube channel. Note that these logical identities are also found in Boolean algebra and each of … Read more

Prepositional Logic – Duality

We know that the simple statements are represented as p, q and so on. Suppose we are given a compound preposition. There is another property of compound prepositions called the duality; Therefore, the dual of above statement is The dual can be achieved by interchanging by or interchanging by . This means and is dual … Read more

Finite Probability

Finite Probability is a very important concept in discrete mathematics. Before we begin let’s understand some basic terminology, that is important in understanding probability theory. Basic Terminologies Experiment  An experiment is some task you do and get an outcome, possibly from a set of different outcomes. Example, throwing a dice would result in a number between one to … Read more

Logical Equivalence

We have seen prepositions, connectives and compound prepositions; all possible combinations of truth values of the individual prepositions in a compound preposition is depicted in a truth-table. However, it is possible that another preposition or compound preposition has the same truth values in the truth table. This is called logical equivalence of two prepositions. The … Read more

Prepositional Logic-Implication and Biconditional

In the previous video, you learned about different types of basic logical connectives that helps in creating compound prepositions. These connectives are join two or more atomic statements to form compound preposition which also have a truth value of its own. We have discuss negation, conjunction, and disjunction connectives so far, the remaining two connectives … Read more