Calculator Inputs
Example Data Table
| Domain | Predicate P(x) | Quantifier Statement | Outcome | Witness |
|---|---|---|---|---|
| {1, 2, 3, 4, 5, 8, 13} | x > 7 and x mod 2 = 0 | ∃x ∈ D : P(x) | True | 8 |
| {2, 4, 6, 8} | x < 0 | ∃x ∈ D : P(x) | False | None |
| {alpha, beta, gamma} | x contains “mm” | ∃x ∈ D : P(x) | True | gamma |
| {logic, proof, axiom} | length(x) ≥ 6 | ∃x ∈ D : P(x) | True | axiom |
Formula Used
The existential quantifier is written as ∃x ∈ D : P(x). The statement is true when at least one element in domain D makes the predicate P(x) true.
Truth(∃x ∈ D : P(x)) = 1, if there exists at least one x in D with P(x) = 1.
Truth(∃x ∈ D : P(x)) = 0, if every tested x in D gives P(x) = 0.
When you activate several rule rows, the calculator first builds the combined predicate. It then checks each domain value and reports whether the final predicate passes for that value.
How to Use This Calculator
- Choose a domain type and enter values as a list or numeric range.
- Pick whether the final predicate needs all active rules or any active rule.
- Configure one to three rule rows for comparisons, modulo checks, text checks, lengths, or set membership.
- Submit the form to evaluate whether any domain element satisfies the predicate.
- Review the truth result, witnesses, rate, and row-by-row table.
- Export the detailed results with the CSV or PDF buttons.
FAQs
1) What does the existential quantifier mean?
It means “there exists.” A quantified statement is true when at least one domain element satisfies the predicate you test.
2) What is a witness?
A witness is any domain value that makes the predicate true. The calculator lists witnesses so you can see exactly why the existential statement passed.
3) When should I use “all active rules”?
Use it when your predicate contains several conditions joined by “and.” Each witness must satisfy every enabled rule row.
4) When should I use “any active rule”?
Use it when your predicate behaves like an “or” statement. A witness only needs to satisfy one enabled rule row.
5) Can I test text values instead of numbers?
Yes. Switch the domain type to text, then use string match, length compare, or membership rules for word-based predicates.
6) Does the calculator support generated ranges?
Yes. Range mode builds numeric domains from start, end, and step values, then evaluates each generated item automatically.
7) Why can an existential statement be false?
It becomes false when no tested domain element satisfies the full predicate. In that case, the witness list remains empty.
8) What do CSV and PDF exports include?
They include the visible result summary and the evaluation table, making it easier to save classroom work, proof checks, and examples.