A prime attribute of a relation scheme \(R\) is an attribute that appears

Concept: A candidate key of a relation R is a minimal set of attributes that uniquely identifies every tuple of R; a relation can have more than one candidate key. An attribute is called a prime attribute if it belongs to at least one of R's candidate keys — membership in any single candidate key is enough. An attribute belonging to none of R's candidate keys is called non-prime.

Example: Let R(A, B, C, D) have two candidate keys, {A, B} and {A, C}. A appears in both; B appears only in the first; C appears only in the second. All three — A, B, and C — are still prime, because each appears in at least one candidate key. D appears in neither candidate key, so D is non-prime.

Why the other statements do not define a prime attribute:

• "In all candidate keys of R" is too strong — in the example above, B sits in {A, B} but not in {A, C}, so requiring membership in every candidate key would wrongly mark B (and C) as non-prime. If R had two candidate keys sharing no attribute at all, this reading would leave zero prime attributes, which is not how the definition works.

• "In a foreign key of R" confuses two unrelated ideas — a foreign key references a candidate key of another relation and enforces referential integrity; it has no bearing on whether an attribute sits inside one of R's own candidate keys.

• "Only in the primary key of R" is too narrow — the primary key is just the one candidate key a designer picks to enforce as the identifier. An attribute in a different, unchosen candidate key is still prime even though it is absent from the primary key.

Result: So the defining condition is membership in some — at least one — candidate key of R, which matches the correct option.