Description
Return membership under (A minus B) minus C as a&&!b&&!c and under A minus (B minus C) as a&&!(b&&!c), plus whether the results differ.
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 membership under (A minus B) minus C as a&&!b&&!c and under A minus (B minus C) as a&&!(b&&!c), plus whether the results differ.
When to use this tool
Use Set Difference Parenthesis Membership Truth 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 a, b, c. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leftAssociated, rightAssociated, differs. Inspect leftAssociated, rightAssociated, differs before interpreting the associated values.
Return membership under (A minus B) minus C as a&&!b&&!c and under A minus (B minus C) as a&&!(b&&!c), plus whether the results differ.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Boolean. |
| b | B | Required. Boolean. |
| c | C | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leftAssociated | Left Associated | Required. Boolean. |
| rightAssociated | Right Associated | Required. Boolean. |
| differs | Differs | Required. Boolean. |
{
"input": {
"a": true,
"b": true,
"c": true
},
"output": {
"leftAssociated": false,
"rightAssociated": true,
"differs": true
}
}Limitations and assumptions
- These are one element's supplied membership flags. The tool demonstrates parenthesis effects without constructing sets, finding an element witness, or proving whole-set equality.
- 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.
- Cartesian Product Single Pair Membership
Return member when leftElement occurs in left and rightElement in right, with missingFactors naming absent sides.