Description
Return counterexample when witness occurs in first and not in second.
A finite set records membership, while a multiset also records multiplicity. An ordered set adds an ordering rule, and an interval adds endpoint-closure choices. A witness for one element, a count budget, and equality of complete sets establish different facts.
Return counterexample when witness occurs in first and not in second.
When to use this tool
Use Subset Counterexample Single Witness when you need the stated finite-set, interval, multiplicity, membership, or ordering operation under the given equality convention.
How to use the tool and how it works
- Enter first, second, witness. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read counterexample. Inspect counterexample before interpreting the associated values.
Return counterexample when witness occurs in first and not in second.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| second | Second | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| witness | Witness | Required. Text; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| counterexample | Counterexample | Required. Boolean. |
{
"input": {
"first": [
"a",
"b"
],
"second": [
"a"
],
"witness": "b"
},
"output": {
"counterexample": true
}
}Limitations and assumptions
- A false result only says this particular witness fails; it does not prove the subset relation. Membership uses exact supplied strings without normalization or a complete set comparison.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a full set operation when one element or count cannot establish the required relation. Preserve the distinction between strings, typed scalar atoms, nested sets, ordered lists, and multisets.
References
Similar or alternative tools
- set/subset-checker
Set inclusion asks whether every distinct candidate value appears in a supplied superset.
- Finite Set Two Witness Equality Status
Deduplicate both lists, find at most one first-list-only and second-list-only witness, and return equal when neither exists.