LaTeX
(A\cup B)^c=A^c\cap B^cVariables
- A, B: subsets of a universal set
- c: set complement
How to use this formula
Relates the complement of a union to the intersection of complements.
Important notes
- The universal set must be understood.
- A second law exchanges union and intersection.
Quick example
If an element is outside A∪B, it is outside both A and B.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The universal set must be understood.
- Define the universe and the meanings of inclusion, equality, complement, and cardinality used in the expression.
Worked example
If an element is outside A∪B, it is outside both A and B.
Common mistakes
- Before substituting values into De Morgan Law for Sets, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Verify the result of De Morgan Law for Sets with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use De Morgan Law for Sets in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
(A\cup B)^c=A^c\cap B^c. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the De Morgan Law for Sets used for?
Relates the complement of a union to the intersection of complements.
Can I copy this formula as LaTeX?
Yes. Copy (A\cup B)^c=A^c\cap B^c or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.