Posts Tagged ‘antecedent’
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
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
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 »
