ICT 101 Use of Logical Equivalence and Its Features Assessment 4 Answer
In this assignment, we select the topic Logical equivalence. In Logical equivalence two mathematical statements or logics are compared. These statements are compared under some set of formulas and checked for their truth values in a model. The equivalency is then represented by (:: or double arrow) sign. Equivalency are of many types and uses and different from each other but their basic concepts are same.
Logical equivalency is all about to compare two mathematical statements and said that they are equivalent or not based their truth values. It is used to check the equality of a set of mathematical values and compare their relation. It compares their truth values, if the value is same then the statements are logically equivalent and if the truth values are different, the statements are un-equal. This logical equivalence comparison, is used in providing mathematical results by replacing a mathematical expression with alternative equal expression, in this situation, the truth value of the original unit, will not change. We use three types of propositions based on their truth values that are Tautology, contingency and contradiction. A proposition that is anytime a resulted a true value is called Tautology. A proposition that is anytime resulted a false value is called Contradiction and a proposition that will anything from a tautology or a contradiction is called a Contingency
From the above understanding of methods and formulas used to derive logical equivalence propositions, we can take an example to solve a mathematical formula from some pre defined laws. An equation is provided to us that need to be prove for logical equivalency using mathematical method. The provided equation is – ¬ (P → Q) ≡ P ^ ¬ Q. to solve this equation, we consider its left hand side values that is –
¬ (P → Q) ≡ ¬ (¬ P ^ Q) ………………………………………… taken from first equivalence condition
≡ ¬ (¬ P) ^ ¬ Q …………………………………….. derived from De Morgan’s law
≡ P ^ ¬ Q ……………………………………………. Derived from Double negation law
So that, it is proved that the equation id logically equivalent by its left hand side to right hand side values.
Information technology application
There are so many mathematical applications today that are used in the information technology that can ease a complex task. The computer algebra system is one of the most used application or we can say a package of software that is used to resolve maths problems. This application will automatically calculate a difficult algebraic task and solve it within a second. It is slightly different from the traditional calculator by its additional functionality of using numeric values with symbols. Its capabilities may be varied from system to system but the basic functionalities will be remained same. This application has features of graphically design an equation. Its interface delivers a programming language that helps one in designing own tasks as a design and used. This software application is today used by many institutes ad universities that changes their way of teaching mathematics and started using this flexible tool to solve mathematical problems. This application is used to solve functions of rational, polynomials factors, solution of an equation and so many other maths issues. To resolve these type of math problems, it has in built tools like Maple, MathCAD or Mathematica. For example, when we try to solve a simple math problem that is so long to calculate with the help of a calculator and finally shown an error. This daunting task can be easily solved by the help of Maple tool within few seconds and with accuracy in result. We can also track the steps used in resolving a math problem. This software application eliminates the involvement of humans by physically in solving typical mathematical problem and every thing will be manage and derived by using tools and software.
In this assignment, we will discuss the use of logical equivalence and its features. Logical equivalency is sued to compare two mathematical values and check or compare their relation by their truth values. We use three types of propositions based on their truth values that are namely Tautology, contingency and contradiction. There are several methods presents to check the two values are logically equivalent or not. These methods include truth tables, mathematical tables etc. By using these tables, we can easily calculate and derive result of a complex math problem. We preferred to use a mathematical application that is mostly used in information technology today to resolve easy to complex maths problems, is computer algebra system. This software application has so many tools to help resolve maths issues within a second. Today, so many institutes and universities are using this application in their learning and making easy the complex mathematical problems.