Adjective - Having the quality of at-least-one-of-a-subset-ness

Question

For example: let us say we have two form fields, name and surname. Both need to be filled out to complete and submit the form; we say these two fields are required.

We also have two other fields, email and phone number. At least one of them needs to be filled out to submit the form. We say these two fields are (???).

Does English have a singular adjective which expresses this quality? The only one I can think of is disjunctive because the concept is related to logical disjunction (OR). However, having consulted the Cambridge online dictionary it seems the word has a meaning closer to exclusive logical disjunction (XOR).

Answer 1

According to Wikipedia:

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true. The logical connective that represents this operator is typically written as ∨ or +. A∨B is true if A is true, or if B is true, or if both A and B are true. In logic, or by itself means the inclusive "or", distinguished from an exclusive "or", which is false when both of its arguments are true, while an [inclusive] or is true in that case. [Emphasis added.]

If you have two or more fields, at least one of which must be filled in by the user, you are dealing with logical or mathematical disjunction, i.e., inclusive disjunction, where inclusive is implicit unless stated otherwise. You would be on solid ground in characterizing these fields as disjunctive, but few would understand what you're saying. Better to simply say what is required: that a user complete at least one of the following set of two or more fields.

Answer 2

Since a possible mathematical term has already been provided in another answer, I will suggest something that be more applicable to English in general.

The two fields can be described (using an adjectival phrase) as conditionally required (or, conversely, conditionally optional).

Given two options, the first is required only if the second is left empty—and vice-versa.

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Following are several example of this terminology.

From jsonSchema attribute conditionally required, asked by halvete at Stack Overflow:

In certain cases, I would like the messageVersion field not to be mandatory. Is there any way to make the mandatory-ness of the this field conditional?

From Conditionally required property using data annotations, asked by DrCopyPaste at Stack Overflow:

But I want 'Name' field only to be required if 'DocumentType' is equal to 1 and 'Name2' only required if 'DocumentType' is equal to 2 .

From "40 CFR § 158.110 - Required and conditionally required data." at the Legal Information Institute:

(b) Data designated as “conditionally required” (CR) for products with a given use pattern are required by EPA to evaluate the risks or benefits of a product having that use pattern if the product meets the conditions specified in the notes accompanying the requirement. The determination of whether the data must be submitted is based on the product's use pattern, physical or chemical properties, expected exposure of nontarget organisms, and/or results of previous testing (for example, tier testing). Applicants must evaluate each applicable test note for the conditions and criteria to be considered in determining whether conditionally required data must be submitted.

From the discussion thread "conditionally required field" at Nintex:

Is it possible to make a field required based on another fields input at run time?

From "How to make a field conditionally required in Microsoft Dynamics GP 9.0" at Microsoft:

This article discusses a customization that can be used to make a field conditionally required in Microsoft Dynamics GP 9.0. When you make this customization, the User Defined 1 field must be set to a value if the customer is on hold.

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In theory, in the case of the specific example in the question, it could be more precisely described as mutually conditionally required (since there are only two and they directly affect each other). However that longer phrase might sound rather awkward to some people.