"given up" vs abandon

[Alice Nora]

Synonyms Lesson, Advanced Level

ESL/EFL Test #104 "Synonyms for abandon", question 7

Despite current problems, they hadn't ......... their commitment to the idea.

(a) left
(b) given up
(c) departed
(d) deserted

Synonyms Lesson, Advanced Level

ESL/EFL Test #104 "Synonyms for abandon", answer 7

Despite current problems, they hadn't given up their commitment to the idea.

Correct answer: (b) given up

Your answer was: incorrect
Despite current problems, they hadn't departed their commitment to the idea.
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Why not give up or abandon? In my opinion, abandon would suit better in that case. Depart is used to describe an act of moving away, isn't it?

Alice Nora

[Mister Micawber]

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The correct answer, as you can see above, is 'given up'. You answered 'departed', but if 'departed' is to fit into the sentence structure, it must be followed by the preposition 'from'; even then, however, it does not collocate naturally with 'commitment'. 'Abandon' would work, but is not offered as an option.
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Native English teacher at Mister Micawber's