Exists[x, expr]
represents the statement that there exists a value of x for which expr is True.

Exists[x, cond, expr]
states that there exists an x satisfying the condition cond for which expr is True.

Exists[{x1, x2, ...}, expr]
states that there exist values for all the for which expr is True.


  • Exists[x, expr] can be entered as . The character can be entered as EscexEsc or \[Exists]. The variable is given as a subscript.
  • Exists[x, cond, expr] can be entered as .
  • In StandardForm, Exists[x, expr] is output as .
  • Exists[x, cond, expr] is output as .
  • Exists can be used in such functions as Reduce, Resolve, and FullSimplify.
  • The condition cond is often used to specify the domain of a variable, as in xIntegers.
  • Exists[x, cond, expr] is equivalent to Exists[x, cond&&expr].
  • Exists[{x1, x2, ...}, ...] is equivalent to .
  • The value of in Exists[x, expr] is taken to be localized, as in Block.

ExamplesExamplesopen allclose all

Basic Examples (1)Basic Examples (1)

This states that there exists a positive solution to the equation :

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Use Resolve to get a condition on real parameters for which the statement is true:

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Reduce gives the condition in a solved form:

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