# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# FindInstance

FindInstance[expr,vars]
finds an instance of vars that makes the statement expr be True.

FindInstance[expr,vars,dom]
finds an instance over the domain dom. Common choices of dom are Complexes, Reals, Integers, and Booleans.

FindInstance[expr,vars,dom,n]
finds n instances.

## Details and OptionsDetails and Options

• FindInstance[expr,{x1,x2,}] gives results in the same form as Solve: if an instance exists, and if it does not.
• expr can contain equations, inequalities, domain specifications and quantifiers, in the same form as in Reduce.
• The statement expr can be any logical combination of:
•  lhs==rhs equations lhs!=rhs inequations or inequalities expr∈dom domain specifications {x,y,…}∈reg region specification ForAll[x,cond,expr] universal quantifiers Exists[x,cond,expr] existential quantifiers
• With exact symbolic input, FindInstance gives exact results.
• Even if two inputs define the same mathematical set, FindInstance may still pick different instances to return.
• The instances returned by FindInstance typically correspond to special or interesting points in the set.
• FindInstance[expr,vars] assumes by default that quantities appearing algebraically in inequalities are real, while all other quantities are complex.
• FindInstance[expr,vars,Integers] finds solutions to Diophantine equations.
• FindInstance[expr,vars,Booleans] solves Boolean satisfiability for expr.
• FindInstance[expr,vars,Reals] assumes that not only vars but also all function values in expr are real. FindInstance[expr&&varsReals,vars] assumes only that the vars are real.
• FindInstance[,xreg,Reals] constrains x to be in the region reg. The different coordinates for x can be referred to using Indexed[x,i].
• FindInstance may be able to find instances even if Reduce cannot give a complete reduction.
• Every time you run FindInstance with a given input, it will return the same output.
• Different settings for the option RandomSeed->s may yield different collections of instances.
• FindInstance[expr,vars,dom,n] will return a shorter list if the total number of instances is less than n.

## ExamplesExamplesopen allclose all

### Basic Examples  (6)Basic Examples  (6)

Find a solution instance of a system of equations:

 Out[1]=

Find a real solution instance of a system of equations and inequalities:

 Out[1]=

Find an integer solution instance:

 Out[1]=

Find Boolean values of variables that satisfy a formula:

 Out[1]=

Find several instances:

 Out[1]=

Find a point in a geometric region:

 Out[1]=
 Out[2]=