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B1 verb 7分で読める

bevise

練習する例文メモとヒント bevise 30秒で

解説 bevise in your Level:

At the A1 level, you should know that 'bevise' means 'to prove'. It is used when you want to show that something is true. For example, if you say you have a dog, you can 'bevise' it by showing a photo. It is a bit more difficult than the word 'vise' (to show), so you might not use it every day, but it is good to recognize it. You will mostly see it in very simple sentences like 'Jeg kan bevise det' (I can prove it). Think of it as 'showing + evidence'. It is a regular verb, so it follows the standard patterns you are learning for past and present tense.

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At the A2 level, you can start using 'bevise' to talk about facts and simple arguments. You might use it when talking about school or work. For example, 'Han skal bevise, at han har lavet sine lektier' (He must prove that he has done his homework). You should be aware of the past tense 'beviste' and the perfect tense 'har bevist'. At this level, you are learning to connect sentences with 'at' (that), and 'bevise' is a great verb for this: 'Jeg vil bevise, at jeg taler sandt' (I want to prove that I am telling the truth).

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At the B1 level, 'bevise' becomes a very useful word for expressing opinions and discussing more complex topics like news, law, or science. You should be able to use it in different contexts, such as 'bevise sit værd' (prove one's worth) or 'bevise en teori' (prove a theory). You should also start to distinguish it from similar words like 'vise' (show) and 'overbevise' (convince). You will encounter 'bevise' in newspapers and TV news, especially in stories about crime or scientific discoveries. It's important to use it with the correct word order in complex sentences.

At the B2 level, you should use 'bevise' with precision. You understand the nuances between 'bevise', 'påvise', and 'dokumentere'. You can use the passive form 'bevises' in formal writing, such as 'Det kan bevises, at klimaet ændrer sig' (It can be proven that the climate is changing). You are comfortable using it in hypothetical situations: 'Hvis de kunne bevise det, ville de have gjort det for længe siden' (If they could prove it, they would have done it long ago). You also recognize the noun 'bevis' (proof/evidence) and how it relates to the verb.

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At the C1 level, you use 'bevise' in sophisticated academic and professional discussions. You understand its role in formal logic and legal argumentation. You can use it in idiomatic expressions and understand its metaphorical applications in literature. You might use it to discuss the 'bevisbyrde' (burden of proof) in a legal sense. Your use of the verb is natural, and you can easily swap it for more specific synonyms like 'godtgøre' or 'verificere' depending on the register. You are also aware of the historical development of the word and its Germanic roots.

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At the C2 level, you have a complete mastery of 'bevise'. You can use it to articulate subtle philosophical points or complex scientific data. You understand the stylistic impact of choosing 'bevise' over its synonyms in different literary genres. You can use it in all its forms, including rare or archaic constructions, and you can explain the fine semantic differences between 'at bevise noget' and 'at føre bevis for noget'. Your command of the word allows you to use it persuasively in high-level debates, ensuring your arguments are both linguistically and logically sound.

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練習する例文メモとヒント

bevise 30秒で

Bevise is a Danish verb meaning 'to prove' or 'to demonstrate truth'.
It is a regular Group 1 verb: bevise, beviste, bevist.
Commonly used in legal, scientific, and everyday argumentative contexts.
Often followed by a direct object or an 'at' (that) clause.

The Danish verb bevise is a cornerstone of logical reasoning, legal proceedings, and scientific inquiry. At its core, it means to provide evidence or a logical argument that establishes a fact or the truth of a statement. In the Danish language, this word carries a weight of certainty; it is not merely about showing something (vise), but about establishing it as an undeniable reality through proof. Whether you are in a courtroom in Copenhagen or a mathematics classroom in Aarhus, bevise is the tool used to bridge the gap between a hypothesis and a confirmed fact.

Legal Context: In Danish law, the burden of proof is often discussed using the noun form bevisbyrde, but the action is always at bevise. To prove someone's guilt or innocence requires concrete evidence.
Scientific Inquiry: Scientists use experiments to prove their theories. If a result can be replicated, the scientist has managed at bevise their hypothesis to the community.
Everyday Arguments: In daily life, we often use it more casually: "Jeg skal nok bevise, at jeg har ret" (I will certainly prove that I am right).

Det er svært at bevise, hvem der startede skænderiet.
— Common Danish expression regarding disputes

Furthermore, the word is deeply embedded in the Danish educational system. Students in 'Gymnasium' (high school) spend significant time learning how to bevise mathematical theorems, such as Pythagoras' theorem. In these contexts, the word represents a rigorous step-by-step logical deduction. It is also used figuratively, such as when someone wants to 'prove their worth' (bevise sit værd) in a new job or a sports team. This metaphorical use highlights the social aspect of proof: demonstrating competence to gain the trust or respect of others.

Hun formåede at bevise sin uskyld over for politiet.

Emotional Proof: You can also prove your love (bevise sin kærlighed) through actions rather than just words, a common theme in Danish literature.

Using bevise correctly in a sentence involves understanding its relationship with its objects. Most commonly, bevise is followed by a direct object or a subordinate clause starting with 'at' (that). For example, "Jeg kan bevise min teori" (I can prove my theory) uses a noun phrase, whereas "Jeg kan bevise, at jorden er rund" (I can prove that the earth is round) uses a clause. The verb is versatile and can be used across all tenses to describe past, present, or future proofs.

Videnskabsmanden beviste sin hypotese gennem mange forsøg.

Transitive Usage: The verb is transitive, meaning it needs an object. You cannot just say "Jeg beviser" without explaining what you are proving.
Passive Voice: In formal Danish, you might see the passive form bevises. For example: "Det kan bevises matematisk" (It can be proven mathematically).

When using bevise in the perfect tense, it combines with the auxiliary verb have. "Jeg har bevist det" (I have proven it). This is used when the proof has already been established and the result is still relevant. In more complex sentences, you might find it used with reflexive pronouns in very specific, rare contexts, but generally, it remains focused on an external fact or truth. It is also important to distinguish it from overbevise (to convince). While bevise focuses on the evidence, overbevise focuses on the change in someone else's mind.

Vi har allerede bevist, at metoden virker.

Conditional Usage: "Hvis jeg kunne, ville jeg bevise det for dig." (If I could, I would prove it to you.)

In Denmark, bevise is a high-frequency word in media and professional settings. If you watch Danish news programs like TV2 Nyhederne or DR1 Avisen, you will frequently hear it in segments about criminal investigations. Reporters might say, "Politiet forsøger at bevise en sammenhæng mellem de to forbrydelser" (The police are trying to prove a connection between the two crimes). This context highlights the word's association with facts, evidence, and the search for truth.

Anklageren skal bevise skyld hinsides enhver rimelig tvivl.

In the Classroom: Teachers often use the word when asking students to justify their answers. "Kan du bevise din udregning?" (Can you prove/verify your calculation?).
Debates and Politics: Politicians use it to challenge their opponents: "Bevis, at jeres plan vil skabe flere job!" (Prove that your plan will create more jobs!).

Beyond formal settings, bevise appears in everyday social dynamics. You might hear friends challenging each other during a game: "Jeg kan bevise, at jeg er hurtigere end dig!" (I can prove that I am faster than you!). It is also used in the workplace, particularly during performance reviews or when proposing new projects. Employees might feel the need to bevise deres værd (prove their value) to secure a promotion or a permanent contract. This widespread use across different levels of formality makes it an essential word for any B1-level learner to master.

Du behøver ikke at bevise noget over for mig.

One of the most frequent mistakes English speakers make when learning Danish is confusing bevise with its simpler cousin vise. While vise means 'to show' or 'to point out', bevise specifically means 'to prove' with evidence. For instance, you can vise someone a picture, but you beviser that the picture is authentic. Using vise when you mean bevise can make your statement sound weaker or more tentative than intended.

Fejl: Jeg skal nok vise, at jeg har ret. (I will show I am right - weaker)
Korrekt: Jeg skal nok bevise, at jeg har ret.

Bevise vs. Overbevise: Another common error is confusing bevise (prove) with overbevise (convince). You beviser a fact, but you overbeviser a person.
Preposition Errors: Sometimes learners use the wrong preposition. It is usually bevise over for nogen (prove to/before someone), not bevise til nogen.

Additionally, learners often struggle with the past participle bevist. Because it looks like the adjective bevidst (conscious/aware), it can lead to confusion in writing. "Han har bevist det" (He has proven it) vs "Han er bevidst om det" (He is aware of it). Paying close attention to the 'd' in bevidst is crucial for accurate Danish spelling and meaning. Finally, ensure you are using the correct auxiliary verb in the perfect tense; always use have, never være, when forming the past perfect of bevise.

While bevise is the most direct word for 'to prove', Danish offers several nuances depending on the context. Understanding these alternatives can help you sound more like a native speaker and choose the word that fits the specific 'flavor' of proof you are describing. For example, dokumentere is often used in administrative or professional contexts where the proof consists of written documents or records.

Påvise: This means 'to point out' or 'to demonstrate'. It is often used in scientific contexts to show a correlation or a specific finding. "Undersøgelsen påviste en sammenhæng."
Godtgøre: A more formal, often legal term meaning to substantiate or make a case for something. It is common in official letters or legal arguments.
Bekræfte: This means 'to confirm'. While bevise creates the truth, bekræfte simply supports a truth that was already suspected.

Vi skal dokumentere alle vores udgifter.

In academic writing, you might also encounter verificere (to verify) or underbygge (to support/substantiate). Underbygge is particularly useful when you have evidence that supports a claim but might not prove it beyond all doubt. Choosing between these words depends on how much certainty you want to convey. If you are 100% sure and have the evidence to back it up, bevise is your best choice. If you are just showing how something works, demonstrere might be more appropriate.

How Formal Is It?

豆知識

The word is related to the English word 'wise' (to make wise or to show).

発音ガイド

UK /beˈviːsə/

US /bəˈviːsə/

The stress is on the second syllable: be-VI-se.

韻が合う語

spise grise vise prise forlise lise skise brise

よくある間違い

Pronouncing the 'v' like a 'w'.
Making the final 'e' too strong.
Stressing the first syllable.
Missing the long vowel in 'vi'.
Confusing it with 'bevidst'.

難易度

読解 2/5

Easy to recognize in context.

ライティング 3/5

Requires correct spelling of 'bevist' vs 'bevidst'.

スピーキング 3/5

Requires correct stress on the second syllable.

リスニング 2/5

Clear pronunciation usually.

次に学ぶべきこと

前提知識

vise sand fakta vide tro

次に学ぶ

overbevise modbevise bevisbyrde dokumentere påvise

上級

godtgøre verificere underbygge indicium kausalitet

知っておくべき文法

V2 Rule

Nu beviser jeg det. (Not: Nu jeg beviser det.)

Subordinate Clauses

Jeg beviser, at det er sandt. (Use 'at' to link clauses.)

Group 1 Verbs

Bevise (inf), beviser (pres), beviste (past), har bevist (perf).

Passive with -es

Det bevises ofte i laboratorier.

Infinitive with 'at'

Det er svært at bevise.

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レベル別の例文

Jeg kan bevise det.

I can prove it.

Simple S-V-O structure.

Kan du bevise dit navn?

Can you prove your name?

Question form.

Han vil bevise alt.

He wants to prove everything.

Use of modal 'vil'.

Se, jeg beviste det!

Look, I proved it!

Past tense 'beviste'.

Vi skal bevise sandheden.

We must prove the truth.

Modal 'skal'.

Hun har bevist det nu.

She has proven it now.

Present perfect tense.

De beviser ingenting.

They prove nothing.

Present tense.

Vil du bevise det for mig?

Will you prove it to me?

Preposition 'for'.

Han beviste, at han var hurtig.

He proved that he was fast.

Subordinate 'at'-clause.

Du skal bevise, at du er 18 år.

You must prove that you are 18 years old.

Modal + 'at'-clause.

Politiet kan ikke bevise noget.

The police cannot prove anything.

Negative construction.

Jeg har bevist min uskyld.

I have proven my innocence.

Present perfect with noun object.

Hun prøver at bevise sin teori.

She is trying to prove her theory.

Infinitive with 'at'.

Kan de bevise, hvem der gjorde det?

Can they prove who did it?

Interrogative clause.

Vi beviste det for læreren.

We proved it to the teacher.

Past tense + indirect object.

Det er nemt at bevise.

It is easy to prove.

Adjective + infinitive.

Han forsøgte at bevise sit værd på arbejdet.

He tried to prove his worth at work.

Idiomatic 'bevise sit værd'.

Videnskabsmænd har bevist, at rygning er farligt.

Scientists have proven that smoking is dangerous.

Formal present perfect.

Det er svært at bevise en negativ påstand.

It is difficult to prove a negative claim.

Abstract noun object.

Hun beviste sin loyalitet over for firmaet.

She proved her loyalty to the company.

Preposition 'over for'.

Hvordan vil du bevise, at du taler sandt?

How will you prove that you are telling the truth?

Question word 'hvordan'.

Han har endnu ikke bevist sin påstand.

He has not yet proven his claim.

Adverb 'endnu ikke'.

Vi må bevise, at planen virker.

We must prove that the plan works.

Modal 'må'.

De beviste deres uskyld i retten.

They proved their innocence in court.

Past tense in formal context.

Anklageren formåede at bevise motivet bag forbrydelsen.

The prosecutor managed to prove the motive behind the crime.

Complex noun phrase object.

Det kan bevises ved hjælp af statistikker.

It can be proven with the help of statistics.

Passive voice 'bevises'.

Hun har bevist sig selv som en dygtig leder.

She has proven herself as a skilled leader.

Reflexive 'bevist sig selv'.

Eksperimentet beviste endegyldigt hypotesen.

The experiment definitively proved the hypothesis.

Adverb 'endegyldigt'.

Uden vidner er det umuligt at bevise noget.

Without witnesses, it is impossible to prove anything.

Conditional context.

Han beviste sin teori gennem omfattende forskning.

He proved his theory through extensive research.

Prepositional phrase 'gennem'.

Kan du bevise din påstand med fakta?

Can you prove your claim with facts?

Preposition 'med'.

Det er blevet bevist gang på gang.

It has been proven time and time again.

Passive perfect tense.

Artiklen søger at bevise nødvendigheden af politiske reformer.

The article seeks to prove the necessity of political reforms.

Formal academic style.

Matematikeren præsenterede et komplekst bevis for at bevise sætningen.

The mathematician presented a complex proof to prove the theorem.

Noun and verb usage together.

Det påhviler anklagemyndigheden at bevise tiltaltes skyld.

It is the responsibility of the prosecution to prove the defendant's guilt.

Formal legal phrasing.

Han formåede at bevise sin uskyld trods de overvældende indicier.

He managed to prove his innocence despite the overwhelming circumstantial evidence.

Concessive clause with 'trods'.

Forskningen har til formål at bevise kausaliteten mellem de to variabler.

The research aims to prove the causality between the two variables.

Technical vocabulary.

Det er endnu ikke lykkedes nogen at bevise Guldbergs formodning.

No one has yet succeeded in proving Guldberg's conjecture.

Complex sentence structure.

Hun beviste sin intellektuelle overlegenhed i debatten.

She proved her intellectual superiority in the debate.

Abstract metaphorical use.

Det lader sig ikke bevise ad empirisk vej.

It cannot be proven empirically.

Formal 'lader sig ikke' construction.

Filosoffen forsøgte at bevise eksistensen af en objektiv moral.

The philosopher attempted to prove the existence of an objective morality.

Highly abstract context.

Retshistorien er fuld af eksempler på, hvor svært det er at bevise forsæt.

Legal history is full of examples of how difficult it is to prove intent.

Legal terminology 'forsæt'.

Han formåede med sit værk at bevise sin status som tidens førende tænker.

With his work, he managed to prove his status as the leading thinker of the time.

Complex prepositional placement.

At bevise en universel sandhed kræver mere end blot observationer.

Proving a universal truth requires more than just observations.

Gerund-like use of infinitive.

Det empiriske materiale er utilstrækkeligt til at bevise årsagssammenhængen.

The empirical material is insufficient to prove the causal link.

Formal academic vocabulary.

Han har med denne opdagelse bevist sit værd for eftertiden.

With this discovery, he has proven his worth for posterity.

Temporal phrase 'for eftertiden'.

Bevisbyrden hviler tungt på dem, der vil bevise det modsatte.

The burden of proof rests heavily on those who wish to prove the opposite.

Idiomatic legal phrasing.

Man kan ikke bevise Guds eksistens gennem logik alene.

One cannot prove God's existence through logic alone.

Existential sentence.

よく使う組み合わせ

bevise sin uskyld

bevise sit værd

bevise en teori

bevise en påstand

bevise modsætningen

videnskabeligt bevist

matematisk bevise

bevise en sammenhæng

bevise sin kærlighed

bevise sin identitet

よく使うフレーズ

Det må du bevise

— A challenge to someone making a claim.

Du siger, du er hurtig? Det må du bevise!

Hvad vil du bevise?

— Asking for the purpose of an action.

Hvorfor gør du det? Hvad vil du bevise?

Det er svært at bevise

— Acknowledging the difficulty of finding evidence.

Det er svært at bevise, hvem der ringede først.

Bevise over for nogen

— To prove something to a specific person.

Jeg skal bevise det over for dig.

Lad mig bevise det

— Offering to provide proof.

Lad mig bevise, at jeg har ret.

Intet at bevise

— Having reached a state where proof is no longer needed.

Han har intet at bevise længere.

Bevise det modsatte

— To prove the contrary.

Alle troede han ville tabe, men han beviste det modsatte.

Uden at bevise det

— Doing something without providing evidence.

Han påstod det uden at bevise det.

Forsøge at bevise

— Attempting to find proof.

De forsøger at bevise teorien.

Nødt til at bevise

— Being obligated to provide proof.

Jeg er nødt til at bevise min uskyld.

よく混同される語

bevise vs vise

Vise means 'to show', bevise means 'to prove with evidence'.

bevise vs overbevise

Overbevise means 'to convince someone', bevise means 'to establish a fact'.

bevise vs bevidst

Bevidst is an adjective meaning 'conscious', while bevist is the past participle of prove.

慣用句と表現

"Bevise sit værd"

— To show that one is competent or useful.

Den nye spiller skal bevise sit værd.

General

"At føre bevis for"

— A more formal way of saying 'to prove'.

Anklageren førte bevis for hans skyld.

Formal/Legal

"Beviset på"

— The proof of something.

Dette er beviset på vores succes.

General

"Kaste bevisbyrden over på"

— To shift the burden of proof to someone else.

Han kastede bevisbyrden over på modstanderen.

Formal

"Et levende bevis"

— A living proof (a person who embodies a fact).

Han er et levende bevis på, at man kan ændre sig.

General

"Bevisets stilling"

— The state of the evidence.

Bevisets stilling er usikker.

Legal

"Stå som bevis"

— To serve as proof.

Disse ruiner står som bevis på krigen.

Literary

"Fælde bevis"

— A piece of evidence that convicts someone.

Videoen var det fældende bevis.

Legal

"Bevisbyrde"

— Burden of proof.

Bevisbyrden ligger hos politiet.

Legal

"Bevis materiale"

— Evidence material.

De indsamlede alt bevis materiale.

Formal

間違えやすい

bevise vs bevidst

Similar spelling and sound.

Bevidst is an adjective (conscious); bevist is a verb form (proven).

Jeg er bevidst om, at det er bevist.

bevise vs påvise

Similar meaning.

Påvise is more about pointing out a finding; bevise is more about absolute proof.

Han påviste fejlen, men beviste ikke dens årsag.

bevise vs vise

Base word of bevise.

Vise is general (show); bevise is specific (prove).

Vis mig billedet, der beviser det.

bevise vs henvise

Shares the 'vise' root.

Henvise means to refer to something.

Jeg henviser til rapporten for at bevise min pointe.

bevise vs anvise

Shares the 'vise' root.

Anvise means to direct or assign.

Han anviste os en plads.

文型パターン

Jeg kan bevise [noun].

Jeg kan bevise det.

Han beviste, at [clause].

Han beviste, at han var her.

Det er svært at bevise [noun].

Det er svært at bevise hans skyld.

[Noun] har bevist sit værd.

Systemet har bevist sit værd.

Det kan bevises, at [clause].

Det kan bevises, at han løøj.

Det påhviler [person] at bevise [noun].

Det påhviler politiet at bevise skyld.

Uden at kunne bevise [noun]...

Uden at kunne bevise påstanden, trak han den tilbage.

Ved at [verb] søger han at bevise [noun].

Ved at eksperimentere søger han at bevise teorien.

語族

名詞

bevis (proof)

bevisførelse (presentation of evidence)

bevisbyrde (burden of proof)

bevislighed (provability)

動詞

bevise (to prove)

modbevise (to disprove)

overbevise (to convince)

形容詞

beviselig (provable)

bevist (proven)

bevisløs (proofless)

使い方

frequency

Common in media, education, and legal contexts.

よくある間違い

Jeg beviste ham det. → Jeg beviste det over for ham.
You prove something 'over for' (to) someone, not directly to them as an indirect object.
Det er bevidst. → Det er bevist.
'Bevidst' means conscious; 'bevist' means proven.
Jeg vil vise min uskyld. → Jeg vil bevise min uskyld.
'Vise' is too weak; 'bevise' is the correct term for legal proof.
Han har beviset det. → Han har bevist det.
'Beviset' is the noun (the proof); 'bevist' is the past participle.
Jeg overbeviste sandheden. → Jeg beviste sandheden.
You 'overbeviser' (convince) people, but you 'beviser' (prove) facts.

ヒント

Past Participle

Always use 'har bevist' for the perfect tense. The 't' ending is standard for Group 1 verbs.

Legal Language

In legal contexts, 'bevise' is often paired with 'skyld' (guilt) or 'uskyld' (innocence).

The 'd' Trap

Never put a 'd' in 'bevise' or 'bevist'. If you see a 'd', it's likely 'bevidst' (conscious).

Stress Pattern

Remember: be-VI-se. The 'be-' is like a short pickup note.

Use 'Påvise'

Use 'påvise' in scientific reports to sound more academic and precise.

Social Proof

Use 'bevise sit værd' when describing your experience in a job interview.

At-Clauses

'Bevise' is almost always followed by ', at...' in complex sentences. Don't forget the comma!

Related Noun

Learn 'et bevis' (a proof) alongside the verb to expand your range.

Logical Steps

In math, 'bevise' implies a series of steps leading to a conclusion.

Evidence Link

Link 'bevise' to 'evidence' in your mind to remember the meaning.

暗記しよう

記憶術

Think of 'be-vise'. You want to 'be' 'wise' by showing the proof.

視覚的連想

Imagine a detective pointing at a smoking gun. He is 'bevising' the crime.

Word Web

bevis fakta sandhed retssag logik teori videnskab undersøgelse

チャレンジ

Try to use 'bevise' in three different sentences today: one about a fact, one about your skills, and one about a past event.

語源

Derived from the Middle Low German word 'bewisen'.

元の意味： To show, point out, or demonstrate.

Germanic (Indo-European).

文化的な背景

Generally a neutral, factual word. No specific sensitivities.

Similar to 'to prove' but sometimes used where English might use 'to demonstrate' or 'to substantiate'.

The concept of 'bevis' in Soren Kierkegaard's philosophy. Danish crime shows like 'Broen' (The Bridge). Mathematical proofs in Danish textbooks.

実生活で練習する

実際の使用場面

Legal

bevise skyld
bevise uskyld
føre bevis
bevisets stilling

Scientific

bevise en hypotese
bevise en teori
videnskabeligt bevist
eksperimentelt bevise

Academic/Math

bevise en sætning
et matematisk bevis
bevise ved modstrid
logisk bevis

Workplace

bevise sit værd
bevise resultater
dokumentere og bevise
bevise kompetencer

Social

bevise man har ret
bevise noget for nogen
bevise sin loyalitet
bevise det modsatte

会話のきっかけ

"Hvordan kan man bevise, at klimaforandringerne er menneskeskabte?"

"Mener du, at man altid skal bevise sin uskyld?"

"Har du nogensinde skullet bevise dit værd på en ny arbejdsplads?"

"Hvad er det sværeste, du nogensinde har måttet bevise?"

"Kan man bevise kærlighed, eller er det bare en følelse?"

日記のテーマ

Skriv om en gang, hvor du beviste, at nogen tog fejl af dig.

Beskriv processen med at bevise en videnskabelig teori.

Hvorfor er det vigtigt at kunne bevise sine påstande i en debat?

Reflektér over udtrykket 'at bevise sit værd'. Føler du et pres for at gøre det?

Hvordan ville verden se ud, hvis vi ikke behøvede at bevise noget?

よくある質問

10 問

Yes, it follows the Group 1 pattern: bevise, beviser, beviste, har bevist.

'Vise' means to show (e.g., show a picture), while 'bevise' means to prove (e.g., prove a crime occurred).

Yes, in the sense of 'bevise sit værd' (prove one's worth) or 'bevise sig selv' (prove oneself).

The Danish word is 'bevisbyrde'.

No, 'beviset' is the definite noun (the proof), whereas 'bevise' is the verb (to prove).

It is neutral and can be used in both formal and informal contexts.

Yes, it is the standard word for proving theorems.

Usually 'over for' (to/before) when proving something to a person.

It can be used as an adjective meaning 'proven', but don't confuse it with 'bevidst' (conscious).

Yes, it is a transitive verb and needs an object or a clause.

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