# Propositional Logic

## For each of these sentences, state what the sentence means if the logical connective or is an inclusive or (that is, a disjunction) versus an exclusive or. Which of these meanings of or do you think is intended?

As usual, we should start with the appropriate definitions. Remember that in mathematics, we must know the definitions before we can start trying to solve a problem. Definitions Let p and q be propositions. The disjunction of p and q, denoted by p ∨ q, is the proposition “p or q.” The disjunction p ∨ …

## ￼Propositional logic Exercise 11. Write these propositions using p and q and logical connectives (including negations)

Solve the following exercise. 11. Let p and q be the propositions p: It is below freezing. q: It is snowing. Write these propositions using p and q and logical connectives (including negations). a) It is below freezing and snowing.b) It is below freezing but not snowing.c) It is not below freezing and it is …

## Propositional Logic: Exercise 7 from the textbook

Suppose that during the most recent fiscal year, the annual revenue of Acme Computer was 138 billion dollars and its net profit was 8 billion dollars, the annual revenue of Nadir Software was 87 billion dollars and its net profit was 5 billion dollars, and the annual revenue of Quixote Media was 111 billion dollars …

## What is the negation of each of these propositions?

In this post, I’ll show some examples of how to negate propositions. As I always recommend, let’s start with the definitions. Definitions Let p be a proposition. The negation of p, denoted by ¬p, is the statement “It is not the case that p.”  The proposition ¬p is read “not p.” The truth value of …

## Which of these sentences are propositions? What are the truth values of those that are propositions?

Propositional logic is a very important topic in Discrete Mathematics. It is part of the foundations every student should know. In this post, I’ll show how I solve this specific type of exercise. In mathematics, definitions are very important. As I always recommend to my students, when you are starting a new topic, and you …

## Negating propositions

A classic exercise in Discrete Mathematics is to negate a given proposition. Here, I’ll explain two things to consider after seeing how many students have problems solving this type of exercise. Background A proposition is a sentence that states a fact. It is True or False but not both. An example of a proposition is …

## Propositional Logic: Exercise 6

The purpose of this post is to explain how to solve this type of exercise. Suppose that Smartphone A has 256 MB RAM and 32 GB ROM, and the resolution of its camera is 8 MP; Smartphone B has 288 MB RAM and 64 GB ROM, and the resolution of its camera is 4 MP, …