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The converse relation does satisfy the (weaker) axioms of a semigroup with involution: () = and () =. [12] Since one may generally consider relations between different sets (which form a category rather than a monoid, namely the category of relations Rel ), in this context the converse relation conforms to the axioms of a dagger category (aka ...
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of ...
The converse is "If a polygon has four sides, then it is a quadrilateral. " Again, in this case, unlike the last example, the converse of the statement is true. The negation is " There is at least one quadrilateral that does not have four sides.
A relation is equal to its converse if, and only if, it is symmetric. A relation is connected if, and only if, its complement is anti-symmetric. A relation is strongly connected if, and only if, its complement is asymmetric. [21] If R and S are relations over a set X, and R is contained in S, then
In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle ... The converse is often included as part of the theorem.
In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied.
The converse of the theorem implies that a homothety transforms a line in a parallel line. Conversely, the direct statement of the intercept theorem implies that a geometric transformation is always a homothety of center O , if it fixes the lines passing through O and transforms every other line into a parallel line.
In geometry, may denote the congruence of two geometric shapes (that is the equality up to a displacement), ... Denote the converse relation of ...