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AllTrue[{e1,e2,…},test]

yields True if test[ei] is True for all of the ei.

AllTrue[expr,test,level]

tests parts of expr at level level.

AllTrue[test]

represents an operator form of AllTrue that can be applied to an expression.

Details
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Examples  
Basic Examples  
Scope  
Properties & Relations  
Possible Issues  
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AllTrue

AllTrue[{e1,e2,…},test]

yields True if test[ei] is True for all of the ei.

AllTrue[expr,test,level]

tests parts of expr at level level.

AllTrue[test]

represents an operator form of AllTrue that can be applied to an expression.

Details

  • AllTrue[list,test] and AllTrue[list,test,level] only evaluate as many test[ei] as are necessary to determine the result.
  • AllTrue[list,test] is equivalent to AllTrue[list,test,1].
  • AllTrue[test][list] is equivalent to AllTrue[list,test].

Examples

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Basic Examples  (4)

Test if all elements of a list satisfy a condition:

Wolfram Language code: AllTrue[{2, 3, 4, 6, 8}, EvenQ]
Wolfram Language code: AllTrue[{2, 4, 6, 8}, EvenQ]

Check if all elements of a matrix satisfy a condition:

Wolfram Language code: AllTrue[{{1, 2, 3}, {4, 5, 6}}, EvenQ, 2]
Wolfram Language code: AllTrue[{{2, 4, 6}, {8, 10, 12}}, EvenQ, 2]

Test if all values of an association satisfy a condition:

Wolfram Language code: AllTrue[<|"a" -> 1, "b" -> 3, "c" -> 5|>, OddQ]

If the condition applied to no element produces False, a symbolic result may be returned:

Wolfram Language code: AllTrue[{2, 6, x, 4, y}, # < 10&]
Wolfram Language code: % /. {x -> 3, y -> 7}

Even when the condition applied to some elements is symbolic, a definitive result may be deduced:

Wolfram Language code: AllTrue[{2, 6, x, 4, y, 15}, # < 10&]

TrueQ may be used to avoid getting a symbolic result:

Wolfram Language code: AllTrue[{2, 6, x, 4, y}, TrueQ[# < 10]&]

Scope  (3)

AllTrue may be applied to expressions with any head:

Wolfram Language code: AllTrue[f[1, 7, 3], OddQ]
Wolfram Language code: AllTrue[f[x, y, z], # < 10&]

AllTrue can operate on ragged expressions:

Wolfram Language code: AllTrue[{{1, 2, 3}, {4, 5}}, IntegerQ, 2]
Wolfram Language code: AllTrue[f[{1, 2, 3}, {4, 5}], IntegerQ, 2]

By default, AllTrue always operates at level 1:

Wolfram Language code: AllTrue[3, EvenQ]
Wolfram Language code: AllTrue[{}, EvenQ]
Wolfram Language code: AllTrue[3, EvenQ, 0]

Properties & Relations  (5)

Compose the predicate with TrueQ to make the predicate stronger:

Wolfram Language code: AllTrue[{x, y, z}, Composition[TrueQ, f]]

AllTrue[list,f] is equivalent to NoneTrue[list,Composition[Not,f]]:

Wolfram Language code: LogicalExpand /@ {AllTrue[{x, y, z}, f], NoneTrue[{x, y, z}, !f[#]&]}

AllTrue[list,f] is equivalent to VectorQ[list,f] when f evaluates to True or False:

Wolfram Language code: AllTrue[Range[10], IntegerQ] VectorQ[Range[10], IntegerQ]
Wolfram Language code: AllTrue[{x, y, z}, # < 10&] VectorQ[{x, y, z}, # < 10&]

AllTrue[list,f] works efficiently on sparse vectors:

Wolfram Language code: AllTrue[SparseArray[{1000 -> 2}, {1000000000000}], EvenQ]

AllTrue[list,test] checks the parts of list in order, stopping as soon as test returns False:

Wolfram Language code: AllTrue[{1, 2, 3, 4, 5}, (Print[#];OddQ[#])&]

Possible Issues  (1)

A symbolic result may be returned:

Wolfram Language code: AllTrue[{x, y, z}, f]
Wolfram Research (2014), AllTrue, Wolfram Language function, https://reference.wolfram.com/language/ref/AllTrue.html (updated 2015).

Text

Wolfram Research (2014), AllTrue, Wolfram Language function, https://reference.wolfram.com/language/ref/AllTrue.html (updated 2015).

CMS

Wolfram Language. 2014. "AllTrue." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/AllTrue.html.

APA

Wolfram Language. (2014). AllTrue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AllTrue.html

BibTeX

@misc{reference.wolfram_2026_alltrue, author="Wolfram Research", title="{AllTrue}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/AllTrue.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_alltrue, organization={Wolfram Research}, title={AllTrue}, year={2015}, url={https://reference.wolfram.com/language/ref/AllTrue.html}, note=[Accessed: 12-June-2026]}