Find out the correct sentence from the following options.

Certain English idiomatic expressions are fixed phrases in which the preposition is fixed by convention and usage, not decided afresh by the ordinary rules that govern free combinations elsewhere in a sentence; the exact preposition has to be learnt along with the phrase.

The idiom for earning a livelihood through hard, honest effort pairs "the sweat of one's brow" with the preposition "by": "he earns his bread by the sweat of his brow" uses "by" to mark the means through which the living is earned, that is, through hard toil. This is the only version of the sentence that reproduces the fixed idiom correctly.

• "with the sweat of his brow" treats sweat as an instrument used directly (as in cutting something "with" a knife), which is not the sense this fixed idiom carries.

• "over the sweat of his brow" borrows a spatial sense of position above something, which does not fit an idiom about the means of earning a living.

• "against the sweat of his brow" suggests opposition or contact against a surface, a sense unrelated to the idiom's meaning of hard-won effort.

Because idiomatic prepositions cannot be swapped for near-synonyms without breaking the expression, the sentence using "by" is the only grammatically and idiomatically correct one among the four.