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A de jure household is characterized by its recognition through legal means, often followed by legal documentation or status. The term "de jure" translates to "by law," highlighting that the household exists based on legal criteria, such as marriage or officially recognized relationships.

In this context, a household where no man is present due to separation or divorce may still be classified as a de jure household. It indicates that the household's structure—despite the absence of one parent—was originally established within a legal framework (i.e., marriage before separation/divorce). This maintains the legal recognition of the household, differentiating it from informal or unregulated living arrangements.

The other options describe different family structures but do not capture the specific legal definition associated with "de jure." A family with both parents actively involved refers to a dual-parent household but does not address the legal aspect. A living arrangement involving multiple unrelated individuals describes a communal or non-familial setup, lacking the legal household recognition typically associated with family units. A household formed through cohabitation indicates an informal arrangement which may not hold legal status unless certain conditions are formally established.

Thus, the correct characterization focuses on the legal structure of the household, which aligns with the understanding of a