Description
Evaluate membership in the symmetric difference of an explicitly supplied finite tuple of set-membership bits.
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.
Evaluate membership in the symmetric difference of an explicitly supplied finite tuple of set-membership bits.
When to use this tool
Use Symmetric Difference Parity 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 membership. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read included, trueCount. Inspect included before interpreting the associated values.
Count true membership entries and return included for odd parity.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| membership | Membership | Required. Array of boolean; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| included | Included | Required. Boolean. |
| trueCount | True Count | Required. Safe integer. |
{
"input": {
"membership": [
true,
false,
true,
true
]
},
"output": {
"included": true,
"trueCount": 3
}
}Limitations and assumptions
- An empty list has count zero and included false. These are one element's flags across a family of sets, not set cardinalities or a constructed union.
- 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
- Symmetric Difference Three Membership Parity
Return member when an odd number of first, second, and third membership flags are true.
- Multiset Symmetric Difference One Count
Return count=abs(firstCount-secondCount) and fromFirst when firstCount is strictly larger, requiring nonnegative integer multiplicities.