Pod pretpostavkom da je davalac krvi spreman, pregled počinje.

Pod pretpostavkom da is a fixed expression meaning assuming that, on the assumption that, or provided that.

In this sentence, it introduces a condition under which something happens:

• Pod pretpostavkom da je davalac krvi spreman, pregled počinje.

A very natural English equivalent would be:

• If the blood donor is ready, the examination begins.
• or more formally, Assuming that the blood donor is ready, the examination begins.

This expression is a bit more formal than a simple ako (if).

Because after the preposition pod, Serbian here uses the instrumental case.

So:

• nominative: pretpostavka = assumption
• instrumental: pretpostavkom

That is why you get:

• pod pretpostavkom = under the assumption / on the assumption

This is one of those combinations you should learn as a set phrase:

• pod uslovom da = provided that
• pod pretpostavkom da = assuming that

So yes, the form pretpostavkom is required by the grammar of the phrase.

The word da introduces a clause, similar to English that in expressions like on the assumption that...

So:

• pod pretpostavkom da = on the assumption that

Then the clause is:

• je davalac krvi spreman = the blood donor is ready

So the full structure is:

• pod pretpostavkom da
  • clause

In Serbian, da is very commonly used to introduce subordinate clauses. Here it is not exactly the same as the English word that in every context, but in this sentence that is the closest function.

Both are possible, but da je davalac krvi spreman is very natural because Serbian often places the clitic je early in the clause.

The verb je here is the 3rd person singular of biti (to be). Short forms like je, sam, si, smo, and so on are clitics, and clitics usually tend to come near the beginning of the clause.

So after da, you often get:

• da je spreman
• da su došli
• da se pregled završi

That said, da davalac krvi je spreman sounds wrong in standard Serbian because the clitic placement is off.

Davalac krvi means blood donor.

It is made up of:

• davalac = giver / donor
• krvi = of blood

The word krvi is the genitive singular of krv (blood).

So literally, this phrase is something like:

• giver of blood

This is a common Serbian pattern:

• čaša vode = glass of water
• karta grada = map of the city
• davalac krvi = donor of blood / blood donor

So krvi is in the genitive because it specifies what kind of donor the person is.

It is a normal and standard expression, especially in medical or administrative contexts.

You will often see:

• davalac krvi = blood donor
• dobrovoljni davalac krvi = voluntary blood donor

It sounds a bit formal because the whole sentence is formal. In everyday speech, people might also rephrase things more simply, but davalac krvi is absolutely correct and common.

Because spreman agrees with davalac, which is:

• masculine
• singular
• nominative

So the adjective must also be:

• masculine singular nominative: spreman

Compare:

• davalac je spreman = the donor is ready
• davateljka je spremna = the female donor is ready
• lice je spremno = the person/entity is ready

Agreement in Serbian is very important: adjectives match the noun in gender, number, and case.

Počinje is the 3rd person singular present tense of počinjati / početi (to begin / start).

Here it means:

• begins
• starts

Serbian often uses the present tense in statements of procedure, instructions, general rules, or scheduled actions. So this sentence sounds like something from a medical protocol or official description:

• Pod pretpostavkom da je davalac krvi spreman, pregled počinje.

This has the feel of:

• Once the donor is ready, the examination begins.
• If the donor is ready, the examination starts.

So even though English might sometimes prefer will begin, Serbian present tense is completely natural here.

Yes. You could say:

• Ako je davalac krvi spreman, pregled počinje.

That means essentially the same thing: If the blood donor is ready, the examination begins.

The difference is mostly in style:

• ako = simpler, more neutral, more everyday
• pod pretpostavkom da = more formal, administrative, or procedural

So the original sentence sounds more official or technical.

The comma separates the introductory subordinate clause from the main clause.

Structure:

• Pod pretpostavkom da je davalac krvi spreman = subordinate clause
• pregled počinje = main clause

So the comma marks the boundary between:

1. the condition
2. the main statement

This is standard Serbian punctuation.

Yes, Serbian word order is fairly flexible, although some versions sound more natural than others.

The original:

• Pod pretpostavkom da je davalac krvi spreman, pregled počinje.

You could also say:

• Pregled počinje pod pretpostavkom da je davalac krvi spreman.

That is also grammatical, but it shifts the emphasis slightly. The original version puts the condition first, which is very natural in formal writing.

What usually should not be changed freely is the placement of the clitic je. So while major parts of the sentence can move, clitic placement still follows rules.

Pregled means examination, check-up, or inspection, depending on context.

In this sentence, because of the medical setting suggested by davalac krvi, it most naturally means:

• medical examination
• screening/check-up before donation

It is a masculine noun, singular, and here it is in the nominative because it is the subject of počinje:

• pregled počinje = the examination begins

It is grammatical and natural, but definitely formal.

A native speaker would easily understand it, especially in a medical, legal, or administrative context. In casual speech, they might prefer something simpler, such as:

• Ako je davalac krvi spreman, pregled počinje.
• Kad je davalac krvi spreman, pregled počinje.

So the original sentence is not wrong or unnatural; it just belongs to a more official register.