De Morgan's Law Calculator
Verified Calculation Engine
The online De Morgan's Law Calculator helps you calculate instantly and solve problems related to Sets Relations Functions. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Verifies De Morgan's laws for sets: (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.
De Morgan's Law 1: (A ∪ B)' = A' ∩ B'
De Morgan's Law 2: (A ∩ B)' = A' ∪ B'
De Morgan's laws relate complement, union, and intersection operations
Inputs
Results
Worked Examples
Example 1: Verify De Morgan's Laws
A = {1, 2, 3}, B = {3, 4, 5}, U = {1, 2, 3, 4, 5, 6}
- setA: [ 1, 2, 3 ]
- setB: [ 3, 4, 5 ]
- universalSet: [ 1, 2, 3, 4, 5, 6 ]
- complementUnion: 6
- intersectionComplements: 6
- complementIntersection: 1, 2, 4, 5, 6
- unionComplements: 1, 2, 4, 5, 6
- law1Verified: true
- law2Verified: true
Example 2: Board Level Problem
A = {2, 4, 6, 8}, B = {4, 6, 8, 10}, U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- setA: [ 2, 4, 6, 8 ]
- setB: [ 4, 6, 8, 10 ]
- universalSet: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
- complementUnion: 1, 3, 5, 7, 9
- intersectionComplements: 1, 3, 5, 7, 9
- complementIntersection: 1, 2, 3, 5, 7, 9, 10
- unionComplements: 1, 2, 3, 5, 7, 9, 10
- law1Verified: true
- law2Verified: true
About this calculator
Overview
De Morgan's Law Calculator evaluates De Morgan's Law for the math / sets-relations-functions library. Primary input cue: Set A [required]: First set (array of elements). Method anchor: De Morgan's Law 1: (A ∪ B)' = A' ∩ B' De Morgan's Law 2: (A ∩ B)' = A' ∪ B'. De Morgan's laws relate complement, union, and intersection operations.
When to use
Use this page when you need de morgan's law from known inputs and want a transparent arithmetic or symbolic check.
Inputs explained
- Set A [required]: First set (array of elements)
- Set B [required]: Second set (array of elements)
- Universal Set [required] — field id `universalSet`
Formula / method
De Morgan's Law 1: (A ∪ B)' = A' ∩ B' De Morgan's Law 2: (A ∩ B)' = A' ∪ B'. De Morgan's laws relate complement, union, and intersection operations (calculator id: de-morgans-law-calculator).
Worked example
Worked values: setA = [1, 2, 3], setB = [3, 4, 5], universalSet = [1, 2, 3, 4, 5, 6] → complementUnion = [6], intersectionComplements = [6], complementIntersection = [1, 2, 4, 5, 6], unionComplements = [1, 2, 4, 5, 6], law1Verified = True, law2Verified = True
Interpreting results
Read the primary output as de morgan's law under the method on this page.
Assumptions
- The wired execution function for `de-morgans-law-calculator` is the source of numerical behavior.
- Inputs for `de-morgans-law-calculator` follow the on-page labels; values/shapes must match this operation.
- Real-number arithmetic is used unless de morgan's law explicitly needs integers.
Limitations
- Display rounding can differ slightly from a CAS/symbolic exact form of de morgan's law.
- Edge cases outside the intended domain of de morgan's law may error or look unstable—treat them as out of scope.
- Complex/branch cuts and undefined points are not always interactively annotated for de morgan's law.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
De Morgan's Law 1: (A ∪ B)' = A' ∩ B' De Morgan's Law 2: (A ∩ B)' = A' ∪ B'. De Morgan's laws relate complement, union, and intersection operations (calculator id: de-morgans-law-calculator).
Example Calculation
Worked values: setA = [1, 2, 3], setB = [3, 4, 5], universalSet = [1, 2, 3, 4, 5, 6] → complementUnion = [6], intersectionComplements = [6], complementIntersection = [1, 2, 4, 5, 6], unionComplements = [1, 2, 4, 5, 6], law1Verified = True, law2Verified = True
Frequently Asked Questions
What is De Morgan's Law Calculator?
- De Morgan's Law Calculator evaluates De Morgan's Law for the math / sets-relations-functions library. Primary input cue: Set A [required]: First set (array of elements). Method anchor: De Morgan's Law 1: (A ∪ B)' = A' ∩ B' De Morgan's Law 2: (A ∩ B)' = A' ∪ B'. De Morgan's laws relate complement, union, and intersection operations.
How does De Morgan's Law Calculator work?
- De Morgan's Law 1: (A ∪ B)' = A' ∩ B' De Morgan's Law 2: (A ∩ B)' = A' ∪ B'. De Morgan's laws relate complement, union, and intersection operations (calculator id: de-morgans-law-calculator).
Why use this Math Numbers calculator?
- Use this page when you need de morgan's law from known inputs and want a transparent arithmetic or symbolic check.