At his age the thought of travelling abroad alone would never ........... my mind.
- have crossed
Which one is correct? Are both possible here?
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The correct phrase is "have crossed".
The sentence is in the present perfect tense, which is formed with the present tense of "to have" and the past participle of the main verb. The past participle of "to cross" is "crossed", so the correct phrase is "have crossed".
In this sentence, the subject is "the thought", so the phrase "have crossed" refers to the idea of traveling abroad alone and how it has entered the speaker's mind over time.
"Cross" alone is not grammatically correct in this sentence.