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Key Facts: Državna Matura Logic Exam

Administered centrally across Croatia by NCVVO (Nacionalni centar za vanjsko vrednovanje obrazovanja).

Governed by the regulatory framework Pravilnik o polaganju državne mature (NN 56/2026).

Total testing time is exactly 150 minutes in a single continuous session.

The total score available is 62 points across multiple-choice, short-response, and formal proof tasks.

The minimum passing score is 30% (18.60 out of 62 points) for the grade dovoljan (2).

Higher grade thresholds: dobar (31.00 pts), vrlo dobar (43.40 pts), and odličan (52.70 pts).

Three blueprint domains: Tradicionalna logika (35%), Logika iskaza (35%), and Predikatna logika i metodologija (30%).

Only writing utensils and a simple drawing ruler are allowed; all electronic devices and calculators are prohibited.

Official exam results are uploaded directly into the national Postani-student portal for university admissions ranking.

The Croatian Državna matura in Logic (Logika) is a 150-minute, 62-point national examination evaluating traditional Aristotelian logic, propositional calculus, predicate logic, and scientific methodology; 18.60/62 points (30%) is required to pass.

Sample Državna Matura Logic Practice Questions

Try these sample questions to review concepts for the Državna Matura Logic exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In traditional logic, what is the relationship between the content (sadržaj) and the scope (opseg) of a concept?
A.Content and scope are directly proportional; increasing content increases scope.
B.Content and scope are completely independent of each other.
C.Content and scope are inversely proportional; increasing content decreases scope.
D.Content refers exclusively to individuals, while scope refers exclusively to essential characteristics.
Explanation: In traditional logic, the law of inverse relationship states that as the content (the set of essential characteristics) of a concept increases, its scope (the set of objects falling under the concept) decreases, and vice versa.
2Which of the following represents the standard logical form of a particular negative (O) categorical proposition?
A.All S are P
B.Some S are not P
C.No S is P
D.Some S are P
Explanation: In classical categorical logic, the four standard forms are designated by vowels: A (universal affirmative: 'All S are P'), E (universal negative: 'No S is P'), I (particular affirmative: 'Some S are P'), and O (particular negative: 'Some S are not P').
3According to the classical Square of Opposition, if the universal affirmative proposition A ('All philosophers are mortal') is TRUE, what is the truth value of the contradictory proposition O ('Some philosophers are not mortal')?
A.True
B.Undetermined
C.Contingent
D.False
Explanation: Contradictory propositions (A and O, or E and I) across the diagonals of the Square of Opposition always possess opposite truth values. If A is true, its contradictory O must be false.
4Which term(s) is/are distributed in a universal negative (E) categorical proposition, such as 'No reptiles are warm-blooded'?
A.Only the subject term
B.Only the predicate term
C.Both the subject and predicate terms
D.Neither the subject nor the predicate term
Explanation: An E proposition asserts complete mutual exclusion between the subject class and predicate class. Therefore, the statement makes an assertion about every member of the subject class and every member of the predicate class, distributing both terms.
5What is the valid immediate inference by simple conversion (obrat) of the particular affirmative proposition 'Some logicians are musicians'?
A.All musicians are logicians.
B.Some logicians are not musicians.
C.No logicians are musicians.
D.Some musicians are logicians.
Explanation: Simple conversion interchanges the subject and predicate without altering quality or quantity. An I proposition ('Some S are P') validly converts simply to an I proposition ('Some P are S').
6Which pair of concepts represents contradictory concepts (proturječni pojmovi) in traditional logic?
A.'Black' and 'White'
B.'Organic' and 'Inorganic'
C.'Triangle' and 'Square'
D.'Teacher' and 'Student'
Explanation: Contradictory concepts (contradictoria) mutually exclude each other and exhaust the entire universe of discourse (A and non-A), leaving no middle ground. 'Organic' and 'Inorganic' form an exhaustive, mutually exclusive dichotomy.
7In a standard categorical syllogism, which figure is characterized by the middle term (M) being the predicate of the major premise and the subject of the minor premise (P-M, M-S)?
A.First Figure
B.Second Figure
C.Fourth Figure
D.Third Figure
Explanation: The Fourth Figure has the middle term as the predicate in the major premise and the subject in the minor premise: P-M, M-S ⊢ S-P. (First Figure is M-P, S-M; Second is P-M, S-M; Third is M-P, M-S).
8Given the premises: 'All mammals are vertebrates' and 'All dogs are mammals', what valid conclusion follows by the First Figure mood Barbara (AAA-1)?
A.Some vertebrates are dogs.
B.All dogs are vertebrates.
C.All vertebrates are dogs.
D.No dogs are non-vertebrates.
Explanation: In Barbara (AAA-1), the major premise is 'All M are P' and the minor premise is 'All S are M', yielding the universal affirmative conclusion 'All S are P' ('All dogs are vertebrates').
9On the classical Square of Opposition, if the universal affirmative proposition A ('All birds can fly') is known to be FALSE, what is the truth value of the contrary universal negative proposition E ('No birds can fly')?
A.True
B.False
C.Undetermined (Unknown)
D.Necessarily False
Explanation: The law of contraries states that two contrary propositions (A and E) cannot both be true simultaneously, but they CAN both be false. Therefore, if one contrary is false, the other remains undetermined (it could be true or false).
10Why does the universal affirmative proposition A ('All swans are white') validly convert only by limitation / per accidens (obrat po prilagodbi) to 'Some white things are swans', rather than by simple conversion to 'All white things are swans'?
A.Because the subject term in an A proposition is undistributed.
B.Because conversion requires changing the quality of the proposition from affirmative to negative.
C.Because particular propositions cannot be derived from universal propositions in traditional logic.
D.Because the predicate term in an A proposition is undistributed and cannot become distributed in the conclusion.
Explanation: In an A proposition ('All S are P'), the subject S is distributed, but the predicate P is undistributed. Simple conversion to 'All P are S' would distribute P in the conclusion, committing the fallacy of illicit distribution. Limiting the quantity to 'Some P are S' keeps P undistributed.

About the Državna Matura Logic Exam

The Državna matura in Logic (Logika) is a standardized national elective examination administered across the Republic of Croatia by the National Centre for External Evaluation of Education (Nacionalni centar za vanjsko vrednovanje obrazovanja - NCVVO). Governed by the regulatory basis Pravilnik o polaganju državne mature (NN 56/2026), the exam assesses student mastery of traditional Aristotelian logic, modern propositional calculus, predicate logic, and scientific methodology as taught throughout Croatian gimnazija curricula (classical, linguistic, and general). The logic examination is highly valued for competitive admission into university faculties including Philosophy (Filozofski fakultet), Law (Pravni fakultet), Mathematics and Natural Sciences (PMF), Computing and Electrical Engineering (FER), and Cognitive Systems. The examination carries 62 scoreable points administered over a single 150-minute testing session. The blueprint encompasses three main domains: Traditional Logic (35%), Propositional Logic (35%), and Predicate Logic & Methodology (30%). Candidates solve both objective multiple-choice questions and constructed-response items requiring truth-table construction, formal symbolic translation, Venn diagrams, and deductive derivations.

Exam sponsor: NCVVO. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

62 questions

Time Limit

150 minutes

Passing Score

18.60 out of 62 points (30%)

Exam / Certification Fees

Free for regular seniors; fee per exam applies for re-sits/external candidates.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

35%

Tradicionalna logika (Traditional Logic)

Concepts, content and scope, pyramidal hierarchy; categorical propositions (A, E, I, O), relations on the square of opposition; immediate inferences (conversion, obversion, contraposition); categorical syllogisms, figures, valid moods, distribution of terms, and Venn diagrams.

35%

Logika iskaza (Propositional Logic)

Propositional logic syntax and semantics, truth functions, complete truth tables, classification of formulas into tautologies, contradictions, and contingencies; equivalence transformations, normal forms, and deductive rules including Modus Ponens, Modus Tollens, and Reductio ad absurdum.

30%

Logika predikata i metodologija (Predicate Logic & Methodology)

Monadic and polyadic predicates, quantifiers, scope, domain of discourse, formalization of quantified statements; formal and informal logical fallacies; scientific definitions, rules of correct definition, division, classification, inductive generalization, and deductive falsification.

Preparing for the Državna Matura Logic Exam

What You Need to Know

  • Passing score: 18.60 out of 62 points (30%)
  • Exam length: 62 questions
  • Time limit: 150 minutes
  • Exam / certification fees: Free for regular seniors; fee per exam applies for re-sits/external candidates. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Državna Matura Logic: Suggested Study Strategy

1Master the Square of Opposition: Ensure you can instantly determine truth values of contrary, contradictory, subcontrary, and subaltern propositions given the truth or falsehood of any single categorical proposition.
2Memorize and apply syllogistic rules: Focus on the distribution of terms (universal propositions distribute their subjects; negative propositions distribute their predicates) to quickly spot illicit major/minor fallacies and undistributed middle terms.
3Practice fast truth-table evaluation: Be fluent in truth functional definitions of implication (P → Q is false only when P is true and Q is false) and equivalence (P ↔ Q is true only when P and Q have identical truth values).
4Drill formal natural deduction rules: Practice conditional proof (CP), indirect proof (Reductio ad Absurdum - RAA), Modus Ponens (MP), and Modus Tollens (MT) until rule application becomes second nature.
5Watch out for quantifier negation equivalences: Remember that ¬(∀x)P(x) is logically equivalent to (∃x)¬P(x), and ¬(∃x)P(x) is logically equivalent to (∀x)¬P(x).
6Distinguish between formal and informal fallacies: Learn to recognize structural formal errors (affirming the consequent, denying the antecedent) versus content-based informal fallacies (ad hominem, ad verecundiam, post hoc ergo propter hoc, circular reasoning).
7Solve full 150-minute past papers from NCVVO: Time management is critical; allocate approximately 40 minutes for traditional logic, 55 minutes for propositional calculus, and 45 minutes for predicate logic and methodology, leaving 10 minutes to review.

Frequently Asked Questions

What is the passing score for the Državna matura Logic exam?

The minimum passing score is 30% of total points, which equals 18.60 out of 62 points to achieve the passing grade dovoljan (2). Higher standard grading cutoffs are: dobar (3) at 50% (31.00 points), vrlo dobar (4) at 70% (43.40 points), and odličan (5) at 85% (52.70 points), verified annually in NCVVO's official post-exam threshold release.

What aids and materials are permitted during the examination?

Candidates are allowed to use standard writing utensils (black or blue ballpoint pen, pencil, eraser) and a simple ruler or geometric triangle for drawing truth tables, Venn diagrams, and derivation trees. No calculators, computers, smartwatches, smartphones, or unauthorized reference sheets are permitted in the testing hall.

How long is the exam and how many points does it contain?

The examination lasts exactly 150 minutes without interruptions and carries a maximum total score of 62 points across multiple-choice, short constructed-answer, and extended logical proof questions.

Which textbooks and standard references form the basis of the Croatian logic matura?

The curriculum is grounded in standard Croatian gymnasium logic textbooks, notably Srećko Kovač's 'Logika' and Gajo Petrović's foundational 'Logika', alongside contemporary symbolic logic standards adhering to classical first-order logic and natural deduction.

Is the Logic examination mandatory for all students?

No, Logic (Logika) is an elective state matura subject (izborni predmet). Students choose to take it based on the specific entrance requirements and ranking criteria of their targeted university faculties, such as philosophy, law, computer science, mathematics, psychology, and cognitive science.

How are deductive proofs and derivations scored?

Extended constructed-response questions requiring formal proofs or truth tables are scored analytically using standard NCVVO rubric keys: partial points are awarded for correctly stating premises, applying valid transformation rules, properly discharging assumptions in conditional proof/reductio, and deriving the sound conclusion.

Does the exam include negative points for incorrect answers on multiple-choice items?

No, there is no negative marking on any part of the Croatian Državna matura. An incorrect response or an unanswered item receives 0 points, meaning candidates should always select an answer for every question.