Description
Return inFirstMinusSecond and disprovesFirstSubset for first-only membership, and disprovesSecondSubset for second-only membership.
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 inFirstMinusSecond and disprovesFirstSubset for first-only membership, and disprovesSecondSubset for second-only membership.
When to use this tool
Use Set Difference Counterexample Role Label 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 inFirst, inSecond. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read inFirstMinusSecond, disprovesFirstSubset, disprovesSecondSubset. Inspect inFirstMinusSecond, disprovesFirstSubset, disprovesSecondSubset before interpreting the associated values.
Return inFirstMinusSecond and disprovesFirstSubset for first-only membership, and disprovesSecondSubset for second-only membership.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| inFirst | In First | Required. Boolean. |
| inSecond | In Second | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| inFirstMinusSecond | In First Minus Second | Required. Boolean. |
| disprovesFirstSubset | Disproves First Subset | Required. Boolean. |
| disprovesSecondSubset | Disproves Second Subset | Required. Boolean. |
{
"input": {
"inFirst": true,
"inSecond": false
},
"output": {
"inFirstMinusSecond": true,
"disprovesFirstSubset": true,
"disprovesSecondSubset": false
}
}Limitations and assumptions
- The flags concern one supplied element. Both false can mean membership in both or neither; that alone does not prove equality or either subset relation.
- 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
- Multiset Symmetric Difference One Count
Return count=abs(firstCount-secondCount) and fromFirst when firstCount is strictly larger, requiring nonnegative integer multiplicities.
- Nested Set Element Versus Subset Label
Distinguish finite-set membership from subset inclusion using JSON scalar atoms and nested arrays, ignoring set order and duplicate elements.