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In propositional logic, modus ponens ( / ˈmoʊdəs ˈpoʊnɛnz /; MP ), also known as modus ponendo ponens (from Latin 'method of putting by placing'), [ 1] implication elimination, or affirming the antecedent, [ 2] is a deductive argument form and rule of inference. [ 3] It can be summarized as " P implies Q. P is true.
In mathematics, Descartes' rule of signs, described by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in its coefficients. The number of positive real roots is at most the number of sign changes in the sequence of polynomial's coefficients (omitting zero coefficients), and the difference ...
Idempotence ( UK: / ˌɪdɛmˈpoʊtəns /, [ 1] US: / ˈaɪdəm -/) [ 2] is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in ...
The rule was known to a number of ancient civilizations, including also the Greek and the Chinese, and was recorded in Mesopotamia as far back as 1800 BCE. [7] For the most part, the Śulvasūtras do not contain proofs of the rules which they describe. The rule stated in the Baudhāyana Śulvasūtra is:
It’s called the 2:1 rule and it’s a hit on TikTok, so we asked a stylist for her take. Meet the Expert Kim Appelt is a fashion stylist , TV personality, author and YouTuber with 11 years of ...
Transformation rules. In logic and philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions ). For example, the rule of inference called modus ponens takes two premises, one in the form "If p ...
Associative property. In mathematics, the associative property[ 1] is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs .
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, = = =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.