Logic is the science of the mind, known since ancient times. It is used by all people, regardless of the place of birth, when they reflect and draw conclusions about something. Logical thinking is one of the few factors that distinguish man from animal. But simply drawing conclusions is not enough. Sometimes you need to know certain rules. The De Morgan formula is one such law.
Brief historical background
Augustus, or August de Morgan lived in the middle of the 19th century in Scotland. He was the first president of the London Mathematical Society, but became famous mainly for his work in the field of logic.
He owns a lot of scientific papers. Among them are works on the topic of propositional logic and the logic of classes. And also, of course, the formulation of the world-famous De Morgan formula, named after him. In addition to all this, August de Morgan wrote many articles and books, including "Logic is Nothing", which, unfortunately, has not been translated into Russian.
The essence of logical science
At the very beginning, you need to understand how logical formulas are built and on what they are based. Only then can one proceed to the study of one of the most famous postulates. In the simplest formulas, there are two variables, and between them a number of signs. Unlike what is familiar and familiar to the average person in mathematical and physical problems, in logic, variables most often have a letter, not a numerical designation and represent some kind of event. For example, the variable "a" could mean "thunder will strike tomorrow" or "the girl is telling a lie", while the variable "b" will mean "it will be sunny tomorrow" or "the guy is telling the truth".
An example is one of the simplest logical formulas. Variable "a" means that "the girl is telling a lie", and variable "b" means that "the guy is telling the truth".
And here is the formula itself: a=b. It means that the fact that the girl is telling a lie is tantamount to the fact that the guy is telling the truth. It can be said that she is only telling a lie if he is telling the truth.
The essence of De Morgan's formulas
It's pretty obvious actually. The formula for De Morgan's law is written like this:
Not (a and b)=(not a) or (not b)
If we translate this formula into words, then the absence of both "a" and "b" means either the absence of "a" or the absence of "b". If ato speak in simpler language, then if both "a" and "b" are not present, then "a" is not present or "b" is not present.
The second formula looks a little different, although the essence remains the same.
(Not a) or (not b)=Not (a and b)
The negation of conjunction is equal to the disjunction of negations.
Conjunction is an operation that in the field of logic is associated with the union "and".
Disjunction is an operation that in the field of logic is associated with the union "or". For example, "either one, or the second, or both at once."
Simple life examples
An example of this is the following situation: you cannot say that learning math is both pointless and stupid only if the study of math is not pointless or stupid.
Another example is the following statement: you cannot say that it will be warm and sunny tomorrow only if tomorrow it will not be warm or tomorrow will not be sunny.
You cannot say that a student is familiar with physics and chemistry if he does not know physics or does not know chemistry.
You cannot say that a man is telling the truth and a woman is telling a lie only if the man is not telling the truth or if the woman is not telling a lie.
Why was it necessary to look for evidence and formulate laws?
De Morgan's formula in logic opened a new era. New options for calculating logical problems have become possible.
Without De Morgan's formula, it has already become impossible to do in such areas of science as physics or chemistry. There is also a type of technology that specializes in working with electricity. There also in some cases scientists use de Morgan's laws. And in computer science, de Morgan's formulas managed to play their important role. The area of mathematics, which is responsible for the relationship with the logical sciences and postulates, is also almost entirely based on these laws.
And finally
Without logic, it is impossible to imagine human society. Most of the modern technical sciences are based on it. And De Morgan's formulas are indisputably an integral part of logic.
