Posts Tagged ‘false’
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 »
Tuesday, October 6th, 2009
Logical Equivalence Explained
Description
A detailed tutorial on logical equivalence. Step by step tutorial with several examples of what logical equivalence is and how to identify it for reference.
Overview
In the study of discrete math, it is said that two statements are logically equivalent if and only if their truth tables match. This means that for every possible combination of the antecedent and the consequent, these two statements must have exactly the same answer in order to be logically equivalent. There is only a true or false answer to this question, there is no “possibly” or “maybe”.
Tags: antecedent, combination, consequent, discrete math, equivalence, equivalent, false, logical, logically, match, Math, same, true, truth table
Posted in Discrete Math | No Comments »
Thursday, September 24th, 2009
How to Solve Proofs by Contraposition
Description
A detailed tutorial on how to solve proofs by contraposition. Step by step tutorial including several example problems of solving proofs by contraposition for reference.
Overview
The method of writing proofs is not entirely a set process – every mathematician brings their own style to their proof, just like an author will bring their own style to their books. However, there are several different basic techniques for writing proofs. One of these is writing proofs by contraposition. A proof by contraposition is by using negation with the antecedent and consequent. You will state that the consequent is false if declared true, and true if declared false. You will then prove that the antecedent is true if it was declared false, or false if it was declared true. If you can prove the contraposition of the statement, then you can also consider that to be the proof of the statement.
Tags: antecedent, consequent, contraposition, discrete math, false, Geometry, Math, negation, proof, proofs, true
Posted in Discrete Math | No Comments »
Thursday, September 24th, 2009
How to Solve Proofs by Contradiction
Description
A detailed tutorial on how to solve proofs by contradiction. Step by step tutorial including several example problems of solving proofs by contradiction for reference.
Overview
The method of writing proofs is not entirely a set process – every mathematician brings their own style to their proof, just like an author will bring their own style to their books. However, there are several different basic techniques for writing proofs. One of these is writing proofs by contradiction. A proof by contradiction is when you take the antecedent and the consequent, and assume the negation of the antecedent – that is to say, say it is false if it is declared true, and true if it is declared false. Then attempt to prove the consequent. If you cannot prove it, then the statement has been proven.
Tags: antecedent, consequent, contradicition, discrete math, false, Geometry, Math, negation, proof, proofs, true
Posted in Discrete Math | No Comments »
Thursday, September 17th, 2009
An Introduction to Truth Value Analysis
Description
A detailed tutorial on the introduction to truth value analysis. Step by step tutorial including several examples of the introduction to truth value analysis for reference.
Overview
Truth value analysis is where you get to use negation, conjunction, disjunction, and implication. You first want to start out by making a truth table. A truth table typically uses the letters P and Q, P as the antecedent or first statement and Q as the consequent or second statement. Then you can write in a statement such as “P implies Q” using either conjunction, disjunction, or implication, and declare it as true or false. Remember how to determine if a statement is true or false:
Conjunction: False ^ False = False, everything else is true
Disjunction: True V True = True, everything else is false
Conditional Implication: True => False = False, everything else is true
Biconditional Implication: True <=> True = True, False <=> False = True, everything is is false
Remember that the statements may look long and complicated sometimes, but each part in it can be broken down into something that is true and something that is false to find out if the entire statement is really true or false.
Tags: conjunction, contrapositive, converse, discrete math, disjunction, false, implication, inverse, Math, negation, true, truth value analysis
Posted in Discrete Math | No Comments »
Thursday, September 17th, 2009
Symbols and Translation: Biconditional Implication
Description
A detailed tutorial on how to translate and symbolize biconditional implication. Step by step tutorial including several examples of how to solve problems with biconditional implication for reference.
Overview
There are two types of implication, conditional and biconditional. This section focuses on biconditional. Biconditional implication is when a statement implies another statement by using the terms “if and only if”, “is necessary for”, and “exactly when”. There are two parts to an implication statement, the antecedent and the consequent. The antecedent implies the consequent. Implication is represented by a symbol that looks like <=>. When the antecedent is true and the consequent true, or when the antedecedent is flase and the consequent is false, then the statement is true. For all other conditions the statement is false.
Tags: bicondition, biconditional, discrete math, false, if, if statement, implication, Math, true
Posted in Discrete Math | No Comments »
Thursday, September 17th, 2009
Symbols and Translation: Conditional Implication
Description
A detailed tutorial on how to translate and symbolize conditional implication. Step by step tutorial including several examples of how to solve problems with conditional implication for reference.
OverviewThere are two types of implication, conditional and biconditional. This section focuses on conditional. Conditional implication is when a statement implies another statement by using the terms “only if”, “on the condition that”, and “implies”. There are two parts to an implication statement, the antecedent and the consequent. The antecedent implies the consequent. Implication is represented by a symbol that looks like =>. When the antecendent is true, and the consequent is false, then the statement is false. For all other conditions the statement is true.
Tags: condition, conditional, discrete math, false, if, if statement, implication, Math, true
Posted in Discrete Math | No Comments »
Thursday, September 17th, 2009
Symbols and Translation: Negation
Description
A detailed tutorial on how to translate and symbolize negation. Step by step tutorial including several examples of how to solve problems with negation for reference.
Overview
Negation is a term used in discrete math that refers to the negation or opposite of a statement, which is represented by the ~ symbol before the statement or letter representing the statement. Negation will change a true statement into a false statement, or a false statement into a true statement. When used in statements instead of letters, the implication of a statement is changed instead of the statement itself.
Tags: discrete math, false, Math, negation, opposite, true, ~
Posted in Discrete Math | No Comments »
Thursday, September 17th, 2009
Symbols and Translation: Conjunction
Description
A detailed tutorial on how to translate and symbolize conjunction. Step by step tutorial including several examples of how to solve problems with conjunction for reference.
Overview
Conjunction is a term used in discrete math that refers to the and statement, which is represented by a symbol that looks a little like the letter A. Conjunction is used when a statement is split into two parts that are being compared to each other. If both the first part of the statement and the second part of the statement are true, then conjunction says that the statement is true. For any other combination, the statement is false.
Tags: and, and statement, conjunction, discrete math, false, Math, true
Posted in Discrete Math | No Comments »
