Math 2.0

Mathematical logic and foundations Definition

Converse

Builds on Implication

Definition

Let pp and qq be propositions. The converse of the implication p→qp \to q is the implication q→pq \to p.

Remarks

An implication and its converse are not logically equivalent. For example, "if n=2n = 2, then nn is prime" is true, but its converse "if nn is prime, then n=2n = 2" is false. The inverse of p→qp \to q is ¬p→¬q\neg p \to \neg q. It is the contrapositive of the converse.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Proposition, concept, no evidence levelPropositionconceptImplication, definition, no evidence levelImplicationdefinitionConverse, definition, no evidence levelConversedefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Proposition concept
  2. Implication definition
  3. Converse definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Converse_(logic), lead section
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