Morgan’s Laws. Declare that the sum of n globally negated (or inverted) prepositional variables is equal to the product of the n individually negated variables and inversely, the product of n globally negated propositional variables is equal to the sum of the n individually negated variables. Formal demonstration if and only if and. for any x: ó Therefore inclusion: ó With propositions. The test uses the associativity and distributivity of the laws and. True Yes true for n.
Summary
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- 1 Universe
- 2 Second Impossible Probability Method
- 3 The rules can be expressed in Spanish as:
- 1 The Propositions
- 2 Logical Connectors
- 4 Morgan Laws allows:
- 1 Cases:
- 5 Sources
Universe
De Morgan’s Laws are a part of Analytical and Propositional Logic, and were created by Augustus De Morgan (Madurai, 1806-London, 1871). In turn, Impossible Probability can be broadly classified into two types of universes, universes of subjects or infinite options, and universes of limited options.
A universe is a set of N elements that form a reality susceptible of statistical study, being able to define the N elements as subjects or options, depending on the type of nature of the elements that form N, a nature whose quantitative quality will reside in the form of measuring its magnitude. Depending on the type of universe to which N belongs, the elements of N can be defined as subjects as options, or they can be defined as limited options a priori.
Second Method of Impossible Probability
The main characteristic of the Second Impossible Probability Method compared to traditional statistics is that, while traditional statistics clearly differentiated from the statistical study based on central tendency or dispersion statistics, for the study of direct scores, the study of relative probability or frequency was strictly reserved for the study of the frequency of a series of options determined in reality, to the extent that by means of the Second Method every subject is susceptible of being studied as an option, and every option as a subject, the universe of infinite subjects or options is understood to be that universe of subjects or options whose direct scores, obtained from the individual measurement of each subject,they are studied by means of probability statistics or statistical probability, by means of the quotient of the direct score, obtained from the individual measurement, of each subject, between the sum of all the direct scores of the entire sample.
In set theory, we find situations in which the considered sets are subsets of some known set, which serves as a reference. Definition Universe set The universal set or universe is the set of all the elements that intervene in the subject or situation of interest. Symbolized U. Example Let the sets be:
- A: The vowels
- B: The consonants
- C: The Spanish alphabet. Vowels and consonants are known to be in the Spanish alphabet, therefore, C is the universe set or C = U. Empty set and unit set. We extend the intuitive notion of sets to the cases of lack of elements and uniqueness of elements by introducing the empty and unitary sets. Empty set and unit set We extend the intuitive notion of sets to cases of lack of elements and uniqueness of elements by introducing n of the empty and unit sets.
Definition Empty set. A set that has no elements is called an empty set and is symbolized by ∅. The empty set is a subset of any set.
The rules can be expressed in Spanish as:
The negation of conjunction is the disjunction of negations. The negation of disjunction is the conjunction of negations. or informally as: “no (A and B)” is the same as “(not A) or (not B)” and also, “no (A or B)” is the same as “(not A) and (not B) ”
The Propositions
A statement is a statement that can receive either a false (F) or a true (V) truth value, but not both. Its denotation is generally found with the letters (p, q, r)
Logical connectors
We can form new propositions from given propositions by using logical connectives. Some of them are: ^ “and” conjunction v “or” disjunction -> “if -, then” implication <-> “if and only if” double implication ¬ “no” negation
Morgan’s laws allow:
They are a part of analytical, prepositional logic, and were created by Augustus de Morgan. They declare the rules of equivalence in which two propositions are shown to be logically equivalent. Morgan’s Laws allow: The change of the conjunction operator into disjunction operator and vice versa. The conjunctive or disjunctive propositions to which Morgan’s laws apply may be affirmed or denied (in whole or in parts).
Cases:
¬ (P ^ Q) ≡ (¬P v ¬Q) If we find a totally denied conjunctive proposition, Morgan’s law allows us to transform it into a disjunctive proposition with each of its members denied
¬ (P v Q) ≡ (¬P ^ ¬Q) If we find a totally denied disjunctive proposition, Morgan’s law allows us to transform it into a conjunctive proposition with each of its denied members
(P ^ Q) ≡ ¬ (¬ P v ¬ Q) If we find an affirmative conjunctive proposition, Morgan’s law allows us to transform it into a disjunctive proposition denied in its entirety and in its members.
(P v Q) ≡ ¬ (¬P ^ ¬Q) If we find an affirmative disjunctive proposition, Morgan’s law allows us to transform it into a conjunctive proposition denied in its entirety and in its members
