The expression "A full-time housewife" can be grammatically classified as a noun phrase.
A noun phrase is a set of words that describe a subject such as a person, place, animal, etc. but does not express a complete idea and due to this, it cannot be classified as a sentence.
The expression focuses on describing a house-wife by using the adjective "full time".
This does not express a complete idea and does not have a verb, so it is a phrase rather than a sentence.
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