Set Builder Calculator
Build multiples roster {x in [start, end] : divisor | x}.
Build multiples roster {x in [start, end] : divisor | x}.
- Grade level
- 6–12
- Curriculum band
- Difficulty
- Beginner
- For this topic
- Time to master
- 1 week
- With daily practice
- Tools on page
- 10 on page
- Calculator + practice
Calculator
Rosters — Set Builder Calculator
Result Summary
Results
Headline
{3, 6, 9, 12, 15, 18}
Roster or verdict
Roster parsing dedupes exactly; Venn regions tile the union; display caps at 24 shown.
Statistics
Live readouts from your current rosters.
Answer size
6
{3, 6, 9, 12, 15, 18}
Visualizations
Region sizes
Overlap share
Formula
Build multiples roster {x in [start, end] : divisor | x}.
Alternative Form
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| A, B | Input sets | rosters | Deduped element lists |
| result | Answer roster | roster | Operation output |
Explanation
Membership decides everything: test each element once against the defining rule.
Derivation
Union adds memberships; intersection ANDs them; difference negates; De Morgan dualizes under complements.
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Parse rosters; dedupe while preserving first order.
Apply the set operation element by element.
Count regions for the Venn diagram.
Cross-check with the counting identity.
Format the roster with cap 24 shown.
State the finished answer.
Worked Examples
See how the calculator works with different scenarios.
Scenario
A = {1,2,3,4}, B = {3,4,5,6}.
Inputs
Calculation
Union {1..6}; both {3,4}
Result
See live roster
Interpretation
Overlap of two drives all regions.
Understanding Your Result
Your Result: Headline: {3, 6, 9, 12, 15, 18}
Typical range: Sizes from 0 (empty) up; Venn regions tile the universe.
What This Means
The headline roster lists exactly the elements satisfying the stated rule — nothing more.
Why It Matters
Filters, joins, permissions and logic gates are set operations in disguise.
Professional Interpretation
Read the missing list for subset verdicts; read neither for coverage gaps.
Recommendations
- •Dedupe inputs first
- •Fix the universe for complements
- •Draw the Venn before coding filters
Learn — The Complete Guide
Set Builder Calculator applies one membership rule to your rosters with Venn proof.
The core concept
Sets are predicates: union ORs, intersection ANDs, complement NOTs.
- Membership decides all
- Venn regions tile U
- Complements need U
Derivations — why the formulas work
Why union adds then subtracts
- 1Count A
- 2Count B
- 3Both counted twice — subtract once
Where you meet this in real life
Learn this first — prerequisites in order
- 1Listing
- 2Venn reading
- 3Multiples
Careers that use this daily
- •Analyst — filters
- •Engineer — queries
- •Designer — logic
- •Admin — permissions
Why it helps
- •Live Venn feedback
- •Roster plus counts
- •De Morgan verification
Best practices
- •Fix U first
- •Keep labels consistent
- •Check neither for coverage
Limitations — what this tool does not do
- •Finite rosters only
- •Text equality (case-sensitive)
Curriculum map — where this topic lives in school
| Level | Grades | Standards | Skills |
|---|---|---|---|
| Middle school | 6–8 | 6.SP | Rosters · Venn |
| High school | 9–12 | HSS-CP | Operations · De Morgan |
Timeline — how this idea grew up
1874
Cantor sets
Set theory founded.
1880
Venn diagrams
Visual logic published.
A little history
- • De Morgan (1847) dualized AND/OR.
- • Zermelo-Fraenkel axiomatized sets.
Exam-day checklist
- • Draw circles
- • Label neither
- • Sum-check regions
Myths vs facts
Practical Tips
- •Comma-separate values
- •Duplicates auto-collapse
- •Fix U for complements
- •Read neither last
- •Copy with share bar
Common Mistakes
Assumptions
This calculator makes the following assumptions to provide estimates:
Limitations
Be aware of these limitations when using this calculator:
Frequently Asked Questions
Answers to common questions about this calculator.
What is set-builder?
This page?
How do I enter sets?
Does it show steps?
Can I print or share results?
Is my data stored?
Related Calculators
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Related Guides
Deepen your understanding with these educational resources.
Glossary
Technical terms used in mortgage calculations explained in plain language.
- Union
- In either set.
- Intersection
- In both sets.
- Complement
- In U but not A.
- Cardinality
- Element count.
- Venn diagram
- Overlapping-circle regions.
Authoritative References
Trusted sources and standards referenced by this calculator.
Applicable Standards
Diagrams & Illustrations
Visual intuition for every core idea. Select a card to enlarge it.
Did You Know?
Short intuition builders — great for class warm-ups.
Venn is 1880
John Venn drew overlapping circles for syllogisms.
∅ is universal subset
Empty set sits inside every set.
De Morgan dualizes
NOT flips AND to OR and back.
Compare Side by Side
Three disjoint regions tile the union — sum equals |union|.
| Region | Part | Count | Note |
|---|---|---|---|
| Only A | 0 | left | A-only |
| Both | 0 | overlap | shared |
| Only B | 0 | right | B-only |
Recent Calculations
Your last runs on this page — stored only in this browser, never uploaded.
Set Builder Calculator: {3, 6, 9, 12, 15, 18}
Current inputs — live
Study Plan
A week-by-week path from prerequisites to mastery. Your checklist progress saves in this browser.
Prerequisites
- ▸Listing elements
- ▸Reading Venn diagrams
- ▸Even/odd multiples
Mastery progress — 0%
- I dedupe automatically
- I fix U first
- I read neither
- 1
Week 1 · ~15 min/day
Operate on sets
Goals
- Union without dupes
- Intersect correctly
- Complement against U
Practice
Five roster ops daily.
Exam tips
- •List regions
- •Check counts sum
Practice Problems
0/3 solvedTry each problem first, peek at the hint only if stuck, then reveal the solution and mark it solved.
A = {1,2,3,4}, B = {3,4,5,6}. Union?
Same sets: intersection?
State De Morgan for union.
Printable Worksheet
Generate a fresh problem set for class or homework. Print it, or copy the answer key separately.
- 1.18 × 47 =
- 2.8 ÷ 11 =
- 3.38 × 26 =
- 4.35 ÷ 4 =
- 5.21 − 16 =
- 6.2 + 26 =
- 7.14 ÷ 12 =
- 8.23 ÷ 3 =
- 9.49 ÷ 7 =
- 10.22 − 17 =
- 11.41 + 18 =
- 12.47 − 35 =
Formula Cheat Sheet
Every formula on this page in one printable table.
| Formula | Meaning | Example |
|---|---|---|
| A ∪ B: in either | Union | {1,2} ∪ {2,3} = {1,2,3} |
| A ∩ B: in both | Intersection | {1,2} ∩ {2,3} = {2} |
| (A ∪ B)′ = A′ ∩ B′ | De Morgan | Dualize under NOT |
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Page Information
2026-09-29
3.1.0-math
Free to use for educational and professional purposes.