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 Book Id: WPLBN0002097038 Subjects: Non Fiction, Education, Smarandache Collections Collections: Math, Literature, Education, Authors Community, Mathematics ► Abstract Full Text Search Details...also by Erhus Cniversity Press, dealt almost exclusively with some "basic" consequences of the Smarandache function. In this one, the universe of dis... ...y from the interest and excitement that can be generated by exploring the consequences of such a problem It is a well-known cliche among writers tha... ... some of these problems. In mathematics, one often does not know what the consequences of a statement are. Cnlike a novel however, there are no compl... ... n, where n is the smallest number such that m divides n'. and associated consequences has spawned many new branches of mathematics. A previous volu... ...t occur in n! 0 This function has many uses when dealing with some of the consequences of the Smarandache function Sen), most notably, the number of... ... prime, the Smarandache values would form the same 3 x 3 magic square. A logical extension of this problem places a restriction on the numbers. The...
 Book Id: WPLBN0002097122 ► Abstract Full Text Search Details... have your say during question & answer sessions. We are here to ferret out logical reasons for the presumed universal, impenetrable light barrier t... ...a cooperative process. There are those who say the reasons don't have to be logical. I, for one, find that smacks of religion, not science. We are... ... USA smarand@unm.edu Abstract: In this short paper, as an extension and consequence of the Einstein-Podolski-Rosen paradox and Bell's inequality... ...rrent theories of string-M theory and the theory of the big bang simply use logically inconsistent language. Namely, one cannot introduce geometry i... ...ually follows that Peanuts character around. But now we encounter a popular logical paradox, repeated over-and- over down through the years, generall...
 Book Id: WPLBN0002097108 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...ant role in fuzzy relation equations. While the t-norm i may be interpreted as logical conjunction, the corresponding operation w i may be interpr... ... as logical conjunction, the corresponding operation w i may be interpreted as logical implication. The following basic properties 31 of w i ... ...practice. For example, in fuzzy reasoning [70], when the inference rule and the consequences are known, a problem to determine antecedents to be use... ...sible solutions according to some levels of plausibility is out of the scope of logical reasoning, strictly speaking. However one may for instance... ... 134 there are manifestations which are neither certain nor impossible and consequences of the presence of a given disorder d which are only po... ...n power of the model, we have to refine the non–fuzzy model in such a way that consequences (resp. manifestations) previously expressed as certain ... ...p. certainly absent) remain classified in the same way and where some possible consequences (resp. possibly present manifestations) are now allowed... ...ication, negation and a quantifier for generalization are used. As usual, those logical operators are characterized by the way they operate on the t... ... B ∧ t B ⊆ t A. (16) Introducing also the notation |= for (generalized) logical validity as in [28, 29] by |= A ≡ t A . ( 1 7 ) W...
 Book Id: WPLBN0002097117 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details... related to Untouchability 114 3.3 Some facts about Untouchability and its Consequences even after 57 years of Independence 334 Chapter F... ...in order to understand the multi-dimensional facets of untouchability and its consequences, we have given relevant excerpts from the translation of ... ...Smarandache [55-59]. 23 DEFINITION 1.4.1: In the neutrosophic logic every logical variable x is described by an ordered triple x = (T, I, F) wh... ...sistent logic, which means contradictory sources of information about a same logical variable, proposition or event one has T + I + F > 1. Thu... ...temporary casteist atrocities to analyze the evils of untouchability and its consequences using Fuzzy Cognitive Maps (FCMs) and Neutrosophic Cognit... ...everal cases, those who dare to love across caste lines have to face the dire consequence of death. R 10 – Varnashrama Dharma It was the earl... ... of the Brahmin society must only be Chandalas. So, in this 150 situation, logically you cannot be faulted since you have a place and plenty of e... ...eech of Periyar, 19-12-1973] 3.3 Some facts about Untouchability and its Consequences even after 57 years of Independence Here we give some ... ... Nadu 1920-1940, Koodal Pubishers, Madurai, (1980). 375 34. Periyar Dasan, Logical Analysis of Atheistic Principles of Periyar, unpublished Ph.D ...
 Book Id: WPLBN0002097647 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...se to the reader as the proof requires vitally only the definitions and a logical use of them. A recent paper [27] which studies strictly wild al... ...utative ring II. Proof: Left for the reader to verify as it is an easy consequence of the definition. THEOREM 4.2.2: Let R be a ring. If R is ...
 Book Id: WPLBN0002097103 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...standing/interpretation which might overlap. 2.3 Definition of Neutrosophic Logical Connectives: The connectives (rules of inference, or operator... ...oblem to solve; here we present the easiest ones: One notes the neutrosophic logical values of the propositions A 1 and A 2 by NL(A 1 ) = ( T 1... ...T 1 , I 1 , F 1 ) and NL(A 2 ) = ( T 2 , I 2 , F 2 ). For all neutrosophic logical values below: if, after calculations, one obtains numbers < 0 ... ...cgi?c=connection&f=0&t=255. [27] Le, Charles T. Le, Software for neutrosophic logical operators, Networking by Industry, Inc. Online, http://www.in... ...nt events, then (3) A4: (countable additivity) If are disjoint events (4) 2.2 Consequences of axioms and bayesian inference From these axioms, all o... ...ery important to note that these rules apply only on irreductible propositions (logical atoms) . A proposition is said to be irreductible (or equivale... ... 2000 MSC: 03E99, 03-99, 03B99, 60A99, 62A01, 62-99. Introduction: As a consequence to [1], [3], [4-7] we display the below unusual extension... ... effect to each other. 5. Representing the comes as the consequence of the contradiction between and , therefore ... ...ny contexts as we can, in order to be less-incomplete and discuss some possible consequences. 1. Introduction Upset because none of the logics I knew ...
 Book Id: WPLBN0002097101 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...trongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Prof. Ba... ... this stimulus input vector with FCM matrix, K.C. Lee et al [65] obtain a consequence vector as follows: (0, 0, 0, 0, 0.3, 0, – 0.3, 0.5) × FCM ma... ...3, 0, – 0.3, 0.5) × FCM matrix = (– 0.5, 0, 0.24, 0, – 0.08, 0, 0). The consequence vector may be interpreted such that changes in those three fact... ... vector can be organized into (0, 0, 0, – 0.1, 0.3, 0, – 0.3, .2). Then a consequence vector may be obtained as (– 0.15, .02, 0, – 0.24, 0, –0.12, 0... ...∩ M j ) ⊂ ( ~ Q j ∩ M j ). Here “⊂” stands for fuzzy set inclusion (logical implication). For brevity, fuzzy causal relationship is abbreviate... ...ity, fuzzy causal relationship is abbreviated as FCR in the following. Logical implication has an antecedent (or premise) and a consequent (or con... ...t (or premise) and a consequent (or conclusion). A typical example of the logical implication is “If A, then B”. In the logical implication, there a... ...quence: negation of A (or ¬ A). The FCR is more complicated than the logical implication. 1. Modus tollens does not hold in the FCR. “When mi... ...ble for relations between several concepts are indeterminate). 2. In a logical implication “If A, Then B”, we cannot draw inference in case when ...
 Book Id: WPLBN0002097090 Subjects: Non Fiction, Philosophy, Smarandache Collections ► Abstract Full Text Search Details... Propositions Section 2 The Law of the Excluded Middle Section 3 Logical Equivalence Section 4 Well-Formed Formulas or WFFs Sectio... ...sophic Logic Section 1 Definition of Neutrosphic Logic Section 2 Logical Connectives in Neutrosophic Logic Section 3 Algebraic Propertie... ... 1 Classical Logic Section 1 Propositions In classical logic, a logical variable is restricted to the values of true(T) and false(F). The ... ...ry in the result column, there are 2 n different Boolean functions for n logical variables. Given the truth values in the column above the 5, ... ...on 1.1.4: In the expression p → q, p is known as the antecedent and q the consequence. The implication is often described as the if-then connective. ... ...on ( p /\ q ) \/ ( ¬ p /\ ¬q ). The ↔ connective can also be considered logical equality. Exclusive or (^) can be considered logical inequality ... ...is no middle between the two “extreme” values of true and false. One consequence of this law is the concept of a vacuous proof. What this means ... ...It is interpreted as a statement that if the antecedent is true, then the consequence is also true. The statement is then false if the antecedent is... ...also true. The statement is then false if the antecedent is true, but the consequence is false. With this notion, if it is not possible to prove the...
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