# Discrete Math

## Prepositional Logic – Duality

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

## Prepositional Logic – Logical Connectives and Truth Tables

Introduction We learned about the statements which has a truth value. A statement can be True or False, but not both. You can make new statements from simple statements, such a statement is called a Compound Preposition or a Compound Statement. For example, Let  p and q be two statements. p:  The triangle has three …

## Preposition Logic – Negation of a Statement

Introduction If p is a statement , then the negation of the statement is negative of the statement. Suppose p is “I am hungry” . The negation of the statement is “not p” where not is the negation operator. There is another way we can represent the negation operator. is the simple preposition, then is …

## Prepositional Logic – Simple Statements

Introduction 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 ‘Statements”. A sentence qualify as a statement when it has a truth value. There is only two truth value …

## How to create a Hasse Diagram

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 is a …

## Permutation and Combination Problems

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 it? A  …

## Semi-Group and Monoid

A set of element S with binary operation * is semi-group if two of the property is satisfied 1. Since, S is a set with binary operation, it should satisfy closure property.       i,e.,  a,b ∈ S, then a * b ∈ S 2. It must satisfy associative property.       i.e., …

## Preposition Logic and Problems – III

Preposition Logic and Problems

## Prepositional Logic and Problems – II

In the previous post , we learned about the prepositional statements and truth tables. You can visit the first post by clicking here. Tautology Formal definition of Tautology, “It is a statement which is True for all it’s variable values”. Meaning, It is a compound statement and each of it’s variable has a truth value …

## Prepositional Logic Formulas and Problems – I

Prepositional Logic is part of logic and deals with truth values of prepositions whether they are true or false. Hence it very useful in proving program correctness and other area where prepositional logic is applied. Some common terminology used in prepositional logic are as follows. Atomic Statements Any simple statement that has a truth value …