Exists

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[, , ... , 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 ex or \[Exists]. The variable x 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 x Integers.

Exists[x, cond, expr] is equivalent to Exists[x, cond && expr].

Exists[, , ... , ... ] is equivalent to .

The value of x in Exists[x, expr] is taken to be localized, as in Block.

See Section 3.4.11.

See also: ForAll, FindInstance, Resolve, Reduce, Element, Eliminate.

New in Version 5.0.

Further Examples