# Discrete Math

## Logical Equivalence – Identity Law

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12 total views 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 …

## List of Logical Equivalences and Truth Tables

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27 total views 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 …

## Prepositional Logic – Duality

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68 total views 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 …

## Finite Probability

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7 total views 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 …

## Logical Equivalence

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32 total views 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 …

## Prepositional Logic-Implication and Biconditional

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47 total views 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 …

## Prepositional Logic – Negation of Statements

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42 total views From the previous article, you know that a prepositional statement can have truth value and the values are boolean – true or false. A statement having true value can be negated using ‘not‘ operator and then its value becomes false or vice-versa. Consider the following example where variable p is the statement “I …

## Prepositional Logic – Simple Statements

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41 total views Prepositional Logic is kind of logic that studies “Statements” and derives relationship among those statements. What is a statement or a preposition ? When we talk, we make many sentences, but all sentences are not . A sentence qualifies as a statement when it has a truth value. There is only two truth …

## How to create a Hasse Diagram

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75 total views Hasse Diagram is created for POSET or Partially Ordered Set. It means that there is a set of elements in which certain element are ordered, sequenced or arranged in some way. It is usually denoted as ≤, this is not “Less than, Equal to”, this symbol shows that elements are ordered. Now, there …

## Permutation and Combination Problems

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0 total views Permutation is arrangement of n objects taken r at a time. You keep arranging them by taken r number of objects at a time or take n objects at a time. Consider 4 objects –  A , B ,C, D  and 2 places 1 ,2, 3 . How many way can you arrange …