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Mathematics vocabulary · Sets and Logic

Converse

Meaning in mathematics, with examples

/ˈkɑːnvɜːrs/nounCommon term

In mathematics, converse means: The statement you get by swapping the 'if' part and the 'then' part of a conditional; the converse of 'if p, then q' is 'if q, then p'.

In Turkish: karşıt önerme, karşıt

How it is used

A theorem can be true while its converse is false, so the converse must be proved separately. Don't confuse it with the 'inverse' (if not p, then not q) or the 'contrapositive' (if not q, then not p), which is always equivalent to the original.

Example sentences

  1. The converse of the Pythagorean theorem is also true.

  2. 'If a number is divisible by 4, it is even' is true, but its converse is false.

Common collocations

  • the converse of
  • the converse is false
  • prove the converse
  • converse and contrapositive
  • if and only ifA phrase joining two statements that are either both true or both false, so that each one implies the other; written ⇔ or 'iff'.
  • theoremAn important mathematical statement that has been proved to be true, such as the Pythagorean theorem.
  • counterexampleA single example that shows a general statement is false; for the claim 'all prime numbers are odd', the number 2 is a counterexample.
  • proofA logical argument that shows, step by step from accepted facts, that a mathematical statement is always true.

More terms: Sets and Logic

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