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Absorption ○ᴸᴼᴳᴵꟲ｜Definition｜1st｜20260105164355-00-⌔

Absorption (logic) - Wikipedia

Absorption (logic)

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Absorption is a valid argument form and rule of inference of propositional logic.¹² The rule states that if $P$ implies $Q$, then $P$ implies $P$ and $Q$. The rule makes it possible to introduce conjunctions to proofs. It is called the law of absorption because the term $Q$ is “absorbed” by the term $P$ in the consequent.³ The rule can be stated:

• ✤ $\frac{P\to Q}{\therefore P\to (P\wedge Q)}$

where the rule is that wherever an instance of "$P\to Q$" appears on a line of a proof, "$P\to (P\wedge Q)$" can be placed on a subsequent line.

Printed 2026-06-28.

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Footnotes

1. Copi, Irving M.; Cohen, Carl (2005). Introduction to Logic. Prentice Hall. p. 362. ↩

2. “Rules of Inference”. ↩

3. Whitehead and Russell, Principia Mathematica, p. 14. ↩

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