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Converse, Inverse, Contrapositive Given an if-then statement "if p , then q ," we can create three related statements: A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause.


Inverse of a Conditional. Negating both the hypothesis and conclusion of a conditional statement.For example, the inverse of "If it is raining then the grass is wet" is "If it is not raining then the grass is not wet".


Inverse definition, reversed in position, order, direction, or tendency. See more.


Opposite in effect. The reverse of. The inverse of adding 9 is subtracting 9. The inverse of multiplying by 5 is dividing by 5. There are many inverses in mathematics!


In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion.These transformations preserve angles and map generalized circles into generalized circles, where a generalized circle means either a circle or a line (loosely speaking, a circle with infinite radius).


If f is an invertible function with domain X and range Y, then − (()) =, for every ∈. Using the composition of functions we can rewrite this statement as follows: − ∘ =, where id X is the identity function on the set X; that is, the function that leaves its argument unchanged.In category theory, this statement is used as the definition of an inverse morphism.


Inverse function definition by Duane Q. Nykamp is licensed under a Creative Commons Attribution-Noncommercial-ShareAlike 4.0 License. For permissions beyond the scope of this license, please contact us .


In mathematics, inverse operations are operations that 'undo' each other. Most operations have an inverse. This lesson describes the most common operations and their inverses, and it provides some ...


Contrapositive. Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."


The converse in geometry applies to a conditional statement. In a conditional statement, the words "if" and "then" are used to show assumptions and conclusions that are to be arrived at using logical reasoning. This is often used in theorems and problems involving proofs in geometry.