Set Intersection Calculator
Shared elements present in both A and B.
Shared elements present in both A and B.
- 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 Intersection Calculator
Result Summary
Results
Headline
{3, 4}
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
2
{3, 4}
Visualizations
Region sizes
Overlap share
Formula
Shared elements present in both A and B.
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, 4}
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 Intersection 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.
Disjoint sets?
Use?
How do I enter sets?
Does it show steps?
Can I print or share results?
Is my data stored?
Related Calculators
Explore more calculators related to this topic.
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 Intersection Calculator: {3, 4}
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.