Absorption Laws (Set Theory)

Theorem

These two results together are known as the , corresponding to the equivalent results in logic.


Union Absorbs Intersection

$S \cup \paren {S \cap T} = S$


Intersection Absorbs Union

$S \cap \paren {S \cup T} = S$


Corollary

$S \cup \paren {S \cap T} = S \cap \paren {S \cup T}$


Sources

  • 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems: Exercise $3$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): absorption laws
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): absorption laws
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): absorption laws
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): absorption laws
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