Absorption Laws (Set Theory)

Theorem

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

Union with Intersection

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

Intersection with 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