Define inverse relation
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Answers
Step-by-step explanation:
In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if X and Y are sets and L ⊆ X × Y is a relation from X to Y, then LT is the relation defined so that y LT x if and only if x L y. In set-builder notation, LT = {(y, x) ∈ Y × X | (x, y) ∈ L}.
The notation is analogous with that for an inverse function. Although many functions do not have an inverse, every relation does have a unique converse. The unary operation that maps a relation to the converse relation is an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or, more generally, induces a dagger category on the category of relations as detailed below. As a unary operation, taking the converse (sometimes called conversion or transposition) commutes with the order-related operations of the calculus of relations, that is it commutes with union, intersection, and complement.
The converse relation is also called the or transpose relation— the latter in view of its similarity with the transpose of a matrix.[1] It has also been called the opposite or dual of the original relation,[2] or the inverse of the original relation,[3][4][5] or the reciprocal L° of the relation L.[6]
Other notations for the converse relation include LC, L–1, L~, {\displaystyle {\breve {L}}}, L°, or L∨.
Answer:
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Step-by-step explanation:
An inverse correlation, also known as negative correlation, is a contrary relationship between two variables such that when the value of one variable is high then the value of the other variable is probably low.