+ P The converse of the statement is, If the grass is wet, then it is raining. However, the weaker statement "Some mammals are cats" is true. : is a right angle, then "[8] For E propositions, both subject and predicate are distributed, while for I propositions, neither is. , then the angle opposite the side of length a a However, if the statement S and its converse are equivalent (i.e., P is true if and only if Q is also true), then affirming the consequent will be valid. a ∈ b × = and R ⊂ . 2 {\displaystyle P\subset Q} However, as with syllogisms, this switch from the universal to the particular causes problems with empty categories: "All unicorns are mammals" is often taken as true, while the converse per accidens "Some mammals are unicorns" is clearly false. , ( 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 original statement. In Mathematical Geometry, a Converse is defined as the inverse of a conditional statement. {\displaystyle a} For example, the Four-vertex theorem was proved in 1912, but its converse was proved only in 1997.[4]. Inference from a statement to its converse per accidens is generally valid. Also find the definition and meaning for various math words from this math dictionary. a A conditional statement ("if ... then ...") made by swapping the "if" and "then" parts of another statement. R {\displaystyle c} . , or "Bpq" (in Bocheński notation). Q If ) , In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. 2 Learn what is converse. } , {\displaystyle R\subseteq A\times B,} The converse, which also appears in Euclid's Elements (Book I, Proposition 48), can be stated as: Given a triangle with sides of length Q In Mathematical Geometry, a Converse is defined as the inverse of a conditional statement. B ( {\displaystyle P\leftarrow Q} , and ) ) ¬ . a {\displaystyle P} c Converse Of Alternate Interior Angles Theorem, Converse Of Basic Proportionality Theorem, Consecutive Interior Angles Converse Theorem. , and Converse. {\displaystyle a^{2}+b^{2}=c^{2}} As an example, for the A proposition "All cats are mammals", the converse "All mammals are cats" is obviously false. ⊆ Consider the statement, If it is raining, then the grass is wet. R {\displaystyle c} The converse of that statement is "If I am mortal, then I am a human," which is not necessarily true. S b It is switching the hypothesis and conclusion of a conditional statement. That is, the converse of "Given P, if Q then R" will be "Given P, if R then Q". Thus, the statement "If I am a triangle, then I am a three-sided polygon" is logically equivalent to "If I am a three-sided polygon, then I am a triangle", because the definition of "triangle" is "three-sided polygon". c ( Note: As in the example, a proposition may be true but have a false converse. a x {\displaystyle \neg Q}. In its simple form, conversion is valid only for E and I propositions:[7]. Let S be a statement of the form P implies Q (P → Q). On the other hand, the converse of a statement with mutually inclusive terms remains true, given the truth of the original proposition. T {\displaystyle a^{2}+b^{2}=c^{2}} x {\displaystyle a} + Switching the hypothesis and conclusion of a conditional statement. then the converse relation ", "The Four Vertex Theorem and its Converse", https://en.wikipedia.org/w/index.php?title=Converse_(logic)&oldid=978919586, Articles with unsourced statements from March 2020, Creative Commons Attribution-ShareAlike License, This page was last edited on 17 September 2020, at 18:33. For example, consider the true statement "If I am a human, then I am mortal." 2 ( The validity of simple conversion only for E and I propositions can be expressed by the restriction that "No term must be distributed in the converse which is not distributed in the convertend. In mathematics, the converse of a theorem of the form P → Q will be Q → P. The converse may or may not be true, and even if true, the proof may be difficult. is a right angle. = Then the converse of S is the statement Q implies P (Q → P). { 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 original statement.[1][2].

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