Description
Return member when an odd number of first, second, and third membership flags are true.
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 member when an odd number of first, second, and third membership flags are true.
When to use this tool
Use Symmetric Difference Three Membership 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 first, second, third. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read member. Inspect member before interpreting the associated values.
Return member when an odd number of first, second, and third membership flags are true.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Boolean. |
| second | Second | Required. Boolean. |
| third | Third | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| member | Member | Required. Boolean. |
{
"input": {
"first": true,
"second": true,
"third": true
},
"output": {
"member": true
}
}Limitations and assumptions
- This is one element's membership in a three-way symmetric difference. It does not inspect sets, count elements, or interpret the flags beyond their supplied boolean values.
- 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 Parity
Evaluate membership in the symmetric difference of an explicitly supplied finite tuple of set-membership bits.
- Multiset Symmetric Difference One Count
Return count=abs(firstCount-secondCount) and fromFirst when firstCount is strictly larger, requiring nonnegative integer multiplicities.