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Graphs such as these are among the objects studied by discrete mathematics, for their interesting mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithms.
The first original Arabic writings on logic were produced by al-Kindi (Alkindus) (805–873), who produced a summary on earlier logic up to his time. The first writings on logic with non-Aristotelian elements was produced by al-Farabi (Alfarabi) (873–950), who discussed the topics of future contingents, the number and relation of the categories, the relation between logic and grammar, and ...
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).
In Islam, the Quran is considered to be the most sacred source of law. [6] Classical jurists held its textual integrity to be beyond doubt on account of it having been handed down by many people in each generation, which is known as "recurrence" or "concurrent transmission" ( tawātur ).
In logic, the law of non-contradiction (LNC; also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that propositions cannot both be true and false at the same time, e. g. the two propositions "the house is white" and "the house is not white" are mutually exclusive.
The propositional calculus [a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic.
The history of logic deals with the study of the development of the science of valid inference ().Formal logics developed in ancient times in India, China, and Greece.Greek methods, particularly Aristotelian logic (or term logic) as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. [1]
Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc.