Posts Tagged ‘P’
Tuesday, October 13th, 2009
How to Identify Contradictions
Description
A detailed tutorial on identifying contradictions. Step by step tutorial including several examples of how to identify contradictions for reference.
Overview
A contradiction is a statement of only false values – one that is false no matter how you look at it. In terms of mathematical logic, it is defined as a propositional form that is false for every assignment of truth values to its components. In order for a statement to be a contradiction, when the proposition is on a truth table it must be false for every possible combination of P and Q.
Tags: components, contradiction, discrete math, false, logic, Math, P, proposition, Q, statement, tautology, true, truth table
Posted in Discrete Math | No Comments »
Tuesday, October 13th, 2009
How to Identify Tautologies
Description
A detailed tutorial on identifying tautologies. Step by step tutorial including several examples of how to identify tautologies for reference.
Overview
A tautology is a statement of truth – one that is true no matter how you look at it. In terms of mathematical logic, it is defined as a propositional form that is true for every assignment of truth values to its components. In order for a statement to be a tautology, when the proposition is on a truth table it must be true for every possible combination of P and Q.
Tags: components, contradiction, discrete math, false, logic, Math, P, proposition, Q, statement, tautology, true, truth table
Posted in Discrete Math | No Comments »
Thursday, October 1st, 2009
An Overview of De Morgan’s Laws
Description
A detailed tutorial of De Morgan’s laws. Step by step tutorial including several examples of De Morgan’s laws for reference.
Overview
De Morgan’s laws refer to the logical process of conjunction and disjunction, more commonly known as “and” and “or”. It deals with the negation of entire statements instead of just parts of a statement. De Morgan’s laws state that:
Not (P and Q) = (Not P) or (Not Q)
Not (P or Q) = (Not P) and (Not Q)
In the past, this has been referred to as “complete negation”. It is impossible to solve negations of logical operators without using De Morgan’s laws.
Tags: and, conjunction, contradiction, contrapositive, converse, De Morgan's laws, De Morgan's Rules, discrete math, disjunction, logical operators, Math, negation, not, or, P, Q
Posted in Discrete Math | No Comments »
Thursday, September 24th, 2009
Identifying the Consequent
Description
A detailed tutorial on the consequent of a conditional. Step by step tutorial including several example problems of identifying the consequent of a conditional for reference.
Overview
A conditional is a statement where something implies something else – that is, the antecedent implies the consequent. In this article, we will be talking about the consequent. The consequent is the last part of the conditional. It is normally expressed as Q, and can either be a numerical expression or a logical expression. The consequent can also contain a second conditional, with its own antecedent and consequent.
Tags: antecedent, conditional, consequent, discrete math, identifying, implies, logical expression, Math, numercial expression, P, Q
Posted in Discrete Math | No Comments »
Thursday, September 24th, 2009
Identifying the Antecedent
Description
A detailed tutorial on the antecedent of a conditional. Step by step tutorial including several example problems of identifying the antecedent of a conditional for reference.
Overview
A conditional is a statement where something implies something else – that is, the antecedent implies the consequent. In this article, we will be talking about the antecedent. The antecedent is the first part of the conditional. It is normally expressed as P, and can either be a numerical expression or a logical expression. The antecedent can also contain a second conditional, with its own antecedent and consequent.
Tags: antecedent, conditional, consequent, discrete math, identifying, implies, logical expression, Math, numercial expression, P, Q
Posted in Discrete Math | No Comments »
Thursday, September 24th, 2009
The Modus Tollens Rule Explained
Description
A detailed tutorial on the modus tollens rule. Step by step tutorial including several example problems of the modus tollens rule for reference.
Overview
Modus tollendo tollens, often simply referred to as modus tollens, is an argument in logic that states if P, then Q. Negation of Q, therefore negation of P. This is sometimes called denying the consequent, and is often confused with the indirect proof of proving by contraposition. There are several forms that the modus tollens rule can take, depending on when and how you are using it.
Logical Operator Notation: 
Basic Form: 
With Assumptions: 
Set Theory:
Predicate Logic:
Tags: assumptions, discrete math, logic, logical operator, Math, modus tollendo tollens, modus tollens, negation, P, predicate, proofs, Q, rule, sequent, set theory, then, therefore, truth tables
Posted in Discrete Math | No Comments »
Thursday, September 24th, 2009
The Modus Ponens Rule Explained
Description
A detailed tutorial on the modus ponens rule. Step by step tutorial including several examples of the modus ponens rule for reference.
Overview
Modus ponendo ponens, typically shortened to just modus ponens, is an argument in logic. It is closely related to the argument modus tollens. Modus ponens states that if P, then Q. P, therefore Q. This can be expressed in either sequent form or rule form for formal notation.
Sequent Form: 
Rule Form: 
Tags: discrete math, logic, Math, modus ponendo ponens, modus ponens, P, proofs, Q, rule, sequent, then, therefore, truth tables
Posted in Discrete Math | No Comments »
