Description
Return before as exclusive-or of inFirst and inSecond, then after with inFirst inverted only when toggleFirst.
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 before as exclusive-or of inFirst and inSecond, then after with inFirst inverted only when toggleFirst.
When to use this tool
Use Symmetric Difference Single Element Toggle 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, toggleFirst. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read before, after. Inspect before, after before interpreting the associated values.
Return before as exclusive-or of inFirst and inSecond, then after with inFirst inverted only when toggleFirst.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| inFirst | In First | Required. Boolean. |
| inSecond | In Second | Required. Boolean. |
| toggleFirst | Toggle First | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| before | Before | Required. Boolean. |
| after | After | Required. Boolean. |
{
"input": {
"inFirst": true,
"inSecond": true,
"toggleFirst": true
},
"output": {
"before": false,
"after": true
}
}Limitations and assumptions
- Only one membership bit is modeled. The tool does not modify a set, verify an element, or compute a complete symmetric difference.
- 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.
- Symmetric Difference Parity
Evaluate membership in the symmetric difference of an explicitly supplied finite tuple of set-membership bits.