A truth table involving n statement variables requires 2 to the power of n rows.

the verdict

SUPPORTED

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Recorded sources

3 sources for · 0 against

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Is it true that a truth table involving n statement variables requires 2 to the power of n rows?

Yes. Multiple reliable references confirm that a truth table with n statement variables requires 2 to the power of n rows to cover all possible combinations of truth values.

Verdict: SUPPORTED · 3 sources for, 0 against · Last checked 4 Oct 2026

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Evidence for · 3

Wikipedia: Truth table

Reference article covering this claim directly

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Wikipedia: Truth table. (n.d.). Wikipedia. https://en.wikipedia.org/wiki/Truth_table

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More for · 2

PLOS (all journals): GPRuler: Metabolic gene-protein-reaction rules automatic reconstruction

Notes the truth table consists of one column for each input variable, for 2^N rows.

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PLOS (all journals): GPRuler: Metabolic gene-protein-reaction rules automatic reconstruction. (n.d.). PLOS (all journals). https://doi.org/10.1371/journal.pcbi.1009550

LibreTexts: LibreTexts: 5.02: Truth Tables Conjunction (and) Disjunction (or) Negation (not)

Explains that a statement with $k$ variables will have a truth table with $2^k$ rows.

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LibreTexts: LibreTexts: 5.02%3A Truth Tables  Conjunction (and) Disjunction (or) Negation (not). (n.d.). LibreTexts. https://math.libretexts.org/Courses/Fullerton_College/Math_100%3A_Liberal_Arts_Math_(Claassen_and_Ikeda)/05%3A_Logic/5.02%3A_Truth_Tables-_Conjunction_(and)_Disjunction_(or)_Negation_(not)

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