Description
Return inUnion=inFirst OR inSecond and disjointAtElement=NOT(inFirst AND inSecond) for the supplied membership flags.
Event probabilities and probability masses lie between zero and one. Marginals, intersections, conditioning events, and endpoint atoms describe different quantities. A probability bound or local consistency check can constrain a model without specifying its complete distribution or dependence structure.
Return inUnion=inFirst OR inSecond and disjointAtElement=NOT(inFirst AND inSecond) for the supplied membership flags.
When to use this tool
Use Finite Event Disjoint Union Membership Flag when you need the stated event identity, boundary policy, distribution component, or local feasibility check.
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 inUnion, disjointAtElement. Inspect inUnion, disjointAtElement before interpreting the associated values.
Return inUnion=inFirst OR inSecond and disjointAtElement=NOT(inFirst AND inSecond) for the supplied membership flags.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| inFirst | In First | Required. Boolean. |
| inSecond | In Second | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| inUnion | In Union | Required. Boolean. |
| disjointAtElement | Disjoint At Element | Required. Boolean. |
{
"input": {
"inFirst": true,
"inSecond": false
},
"output": {
"inUnion": true,
"disjointAtElement": true
}
}Limitations and assumptions
- Disjointness is checked at one element only. A true disjointAtElement value does not establish that the two events are globally disjoint.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Alternative or Complementary methods
Use a full probability table or distribution when a local mass, bound, or identity is insufficient. Specify dependence, conditioning, support order, and endpoint policy before combining terms.
References
Similar or alternative tools
- Event Union Disjointness Correction
For valid marginal probabilities and an intersection within their exact feasible bounds, return union=left+right-intersection and correction=-intersection.
- Censored Event Boundary Mass
Distinguish P(X<t) from P(X<=t) using supplied left-limit and endpoint CDF values.