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In the sentence "My cat’s favorite activity is jumping on the table during dinner," the gerund is "jumping." It functions as a subject complement, specifically describing what the favorite activity is.
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In the sentences you provided:
- In "Vacationing might fulfill your need for relaxation," the gerund is "Vacationing," and it functions as the subject of the sentence.
- In "She dislikes my complaining," the gerund is "complaining," and it functions as a direct object of the verb "dislikes."