Final answer:
The statement is false because 'house' is more neutral and closer to the denotative meaning of a dwelling, whereas 'mansion' implies a large and luxurious residence.
Step-by-step explanation:
The statement that "mansion" most closely matches the denotation among the words: mansion, house, abode, shack, palace is false. The words provided all refer to places where someone might live, but each carries a different connotation reflecting the size, condition, or feeling associated with the dwelling. Mansion and palace imply large, luxurious dwellings, whereas shack conveys a small, often rundown abode. House is the most neutral among these and closest to the basic denotation of a dwelling. Therefore, in terms of the closest denotative meaning, house would be more appropriate as it simply denotes a structure for living without additional connotations of size and luxury.