Build clean mathematical sets from ranges, filters, and logic. See notation, members, and summary instantly. Export every result for homework, revision, and classroom sharing.
| Set Name | Universal Set | Rule | Set Builder Form | Roster Form |
|---|---|---|---|---|
| A | U = {1 to 10} | 3 ≤ x ≤ 7 | A = {x ∈ U | 3 ≤ x ≤ 7} | A = {3, 4, 5, 6, 7} |
| B | U = {1 to 20} | x is even | B = {x ∈ U | x is even} | B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} |
| C | U = {1 to 30} | x is a multiple of 5 | C = {x ∈ U | x is a multiple of 5} | C = {5, 10, 15, 20, 25, 30} |
| D | U = {1 to 20} | x is prime | D = {x ∈ U | x is prime} | D = {2, 3, 5, 7, 11, 13, 17, 19} |
Universal set: U = {x ∈ Z | start ≤ x ≤ end}
Main set: A = {x ∈ U | P(x)}
Cardinality: |A| = number of elements that satisfy P(x)
Complement: Aᶜ = U \ A
Coverage percentage: (|A| / |U|) × 100
Even rule: x mod 2 = 0
Odd rule: x mod 2 ≠ 0
Multiple rule: x mod n = 0
Divisor rule: target mod x = 0
Prime rule: x has exactly two positive factors
Set builder notation helps describe a set with a rule. It is compact. It is precise. It is useful in school maths and higher studies. This calculator turns common number rules into clear notation. It also shows the actual elements. That makes learning easier. You can compare symbolic form with listed values at the same time.
Many learners know the answer but struggle to write it neatly. This tool solves that step. It builds the set builder form from your selected condition. It also creates roster notation. You can see the universal set, the chosen members, and the complement together. This saves time during homework, revision, and classroom practice.
The calculator supports many standard maths rules. You can test ranges, greater than values, and exact equality. You can also generate sets of even numbers, odd numbers, prime numbers, composite numbers, multiples, and divisors. These are common topics in algebra and number theory. The output stays clean and easy to read.
Students often make mistakes with boundaries. Inclusive and exclusive limits can be confusing. This calculator reduces those errors. It shows the interval meaning of your rule. It counts the elements. It reports the minimum and maximum values found. It also calculates the coverage percentage inside the universal set. That adds a useful extra check.
Teachers can use this page to prepare examples quickly. Students can test answers before writing them in notebooks. The example table shows common patterns. The formula section explains the logic behind the results. The membership table adds another learning layer. Each element is marked clearly, so the idea of set membership becomes easier to understand.
You can export the finished result as CSV or PDF. That is helpful for assignments, worksheets, and revision files. The layout is simple. The controls are clear. The content stays focused on maths. If you need a practical set builder notation calculator with roster output and complement analysis, this page gives a strong all in one solution.
Set builder notation defines a set by a rule. Instead of listing every element, it states the property that each element must satisfy inside a universal set.
Roster notation lists every element in the set one by one. It is useful for small or finite sets because the members can be displayed clearly.
The universal set limits the values that can be tested. It gives the calculator a fixed domain, so the resulting set remains finite and easy to analyze.
The complement contains all elements in the universal set that are not in your selected set. It helps you understand what the rule excludes.
Yes. Select the prime condition, define the universal set, and the calculator will return all prime elements within that range in both forms.
Cardinality is the number of elements in a set. The calculator shows the size of the main set, the universal set, and the complement.
Some sets are discrete, not continuous. Even numbers, primes, multiples, and divisors do not fit standard interval notation, so the calculator shows a discrete description instead.
Yes. After entering your values, use the CSV or PDF buttons. The exported file includes the rule, notation, counts, and summary details.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.