ProTeacher

UGC NET Paper 1 – UNIT 6 — LOGICAL REASONING

(For NTA UGC NET Paper I: Teaching & Research Aptitude)

🎯 1. Purpose of this Unit

Logical reasoning checks your ability to analyse arguments, evaluate evidence, and draw valid conclusions.
In NET Paper 1, questions test:

  • The structure of reasoning (statements, premises, conclusions)

  • Valid vs invalid arguments

  • Categorical logic (propositions, syllogisms, square of opposition)

  • Inductive vs deductive logic

  • Venn-diagram validity tests

  • Indian logic (pramāṇas and hetvābhāsas)

🧠 2. Understanding Arguments

2.1 Structure of an Argument

An argument is a group of statements where one (the conclusion) is claimed to follow from the others (the premises).

Example
Premise 1: All students are learners.
Premise 2: Ravi is a student.
∴ Conclusion: Ravi is a learner.

Term Meaning
Premise Evidence / reason offered
Conclusion Claim drawn from premises
Indicator words Therefore, Hence, Thus → conclusion; Since, Because → premise

⚙️ 3. Argument Forms

3.1 Deductive Reasoning

  • Moves from general to specific truth.

  • If premises true → conclusion must be true.

  • Validity matters, not factual truth.

Form:
All A are B. All B are C. ∴ All A are C.
✅ Valid Syllogism

3.2 Inductive Reasoning

  • From particular to general.

  • Conclusion probable, not certain.
    Example: Observed 100 swans white ⇒ “All swans are white.”

3.3 Abductive Reasoning

  • Inference to best explanation.
    Example: Wet road ⇒ Probably rained.

🔢 4. Categorical Propositions

A categorical proposition relates two categories (subject & predicate).

Type Form Example Quantity Quality
A All S are P All dogs are animals Universal Affirmative
E No S are P No dogs are cats Universal Negative
I Some S are P Some students are athletes Particular Affirmative
O Some S are not P Some students are not athletes Particular Negative

🧩 5. Classical Square of Opposition

A (All S are P) ──contradictory── O (Some S are not P)
│ \‾‾‾‾‾‾‾‾‾‾‾/ │
│ contrary │
│ │
E (No S are P) ──contradictory── I (Some S are P)
Relation Meaning
Contradictory Opposite truth values (A ↔ O, E ↔ I)
Contrary Both cannot be true (A & E)
Sub-contrary Both cannot be false (I & O)
Sub-alternation Truth flows downward (A → I; E → O)

⚖️ 6. Mood and Figure of Syllogism

6.1 Mood

Type sequence of propositions (A/E/I/O) for major, minor, conclusion.
Example AAA (Barbara), EAE (Celarent).

6.2 Figure

Determined by position of the middle term (M).

Figure Form Example
1st M–P / S–M ⇒ S–P All men are mortal; Socrates is man ⇒ Socrates mortal.
2nd P–M / S–M ⇒ S–P No reptile is warm-blooded; All snakes are reptiles ⇒ No snake is warm-blooded.

🧮 7. Fallacies (Errors in Reasoning)

7.1 Formal Fallacies (logical structure)

  • Affirming the consequent: p→q, q ⇒ p ❌

  • Denying the antecedent: p→q, ¬p ⇒ ¬q ❌

7.2 Informal Fallacies (content errors)

  • Ad hominem: attacking person not argument.

  • Straw man: misrepresenting opponent’s claim.

  • False cause (post hoc): assuming A→B because A came first.

  • Circular reasoning: premise repeats conclusion.

  • Appeal to authority: treating authority as proof.

💬 8. Language: Connotation and Denotation

Term Meaning Example
Denotation Literal dictionary meaning “Rose” = flower species
Connotation Emotional or associated meaning “Rose” = love, beauty

🔄 9. Analogies

  • Show relation similarity between two pairs.
    Example: Finger : Hand :: Toe : Foot
    Test → Find the same logical relationship (type, function, degree).

🔷 10. Venn Diagrams & Testing Validity

  • Circles represent sets of objects.

  • Use to verify syllogistic arguments.

Example:
All A are B, All B are C ⇒ All A are C ✅
Draw A inside B, B inside C.

Common patterns:

  • Overlapping circles → “some”

  • Separate circles → “none”

  • Nested circles → “all”

🪶 11. Indian Logic (Ānvīkṣikī Tradition)

11.1 Pramāṇa — Means of Valid Knowledge

  1. Pratyakṣa (Perception): Direct sense experience.

  2. Anumāna (Inference): Reasoning from sign to proposition.

  3. Upamāna (Comparison): Knowledge through similarity.

  4. Śabda (Verbal Testimony): Trustworthy authority or scripture.

  5. Arthāpatti (Postulation / Implication): Presumption to explain facts.

  6. Anupalabdhi (Non-apprehension): Knowledge of absence.

11.2 Structure of Anumāna (Inference)

Traditional five steps (Nyāya syllogism):

  1. Pratijñā (Statement): Hill has fire.

  2. Hetu (Reason): Because it has smoke.

  3. Udāharaṇa (Example): Where there is smoke, there is fire (kitchen).

  4. Upanaya (Application): Like that, this hill has smoke.

  5. Nigamana (Conclusion): Therefore hill has fire.

11.3 Vyāpti (Invariable Relation)

  • Universal relation between hetu (reason) and sādhya (conclusion).

  • Example: Smoke → Fire (always co-exist).

11.4 Hetvābhāsas (Fallacies of Inference)

Type Nature Example
Asiddha Unproven reason Sky lotus fragrant (but no lotus exists).
Viruddha Contradictory reason Fire is cold because it is fire.
Satpratipakṣa Counter-reason Hill has no fire because there is water.
Bādhita Opposed by perception Fire is cool (conflicts with experience).
Anaikāntika Inconclusive / non-exclusive Crow visible ⇒ daytime (not always).

🧭 12. Evaluating Deductive vs Inductive Reasoning

Feature Deductive Inductive
Direction General → Specific Specific → General
Strength Certainty (if valid) Probability only
Basis Logic of form Observation & pattern
Example All humans mortal → Socrates mortal 100 crows seen black → All crows black

🔍 13. Common Question Types in NET

  1. Identify valid/invalid argument.

  2. Determine type of proposition (A/E/I/O).

  3. Find contradictory statement.

  4. Use Venn diagram for syllogism.

  5. Spot logical fallacy.

  6. Apply Indian logic (pramāṇa, hetvābhāsa).

  7. Match deductive/inductive features.

  8. Solve analogy pattern reasoning.

🧩 14. Shortcut Revision Map

Concept Key Clue
Argument = Premises + Conclusion Test validity via form
A/E/I/O forms All/No/Some/Some not
Square of Opposition A↔O contradictory
Valid form p→q; p ⇒ q ✔️
Fallacy Form invalid or premise irrelevant
Venn diagram All = subset, Some = overlap, None = disjoint
Indian Logic 6 Pramāṇas, 5 steps of Anumāna, 5 Hetvābhāsas

🧠 15. Preparation Strategy

Step Action
1 Memorize A/E/I/O propositions & square.
2 Practise truth-tables & syllogisms.
3 Draw Venn diagrams for common patterns.
4 Review Indian logic terms daily (Pratyakṣa → Anumāna → Hetvābhāsa).
5 Attempt mock MCQs — mix concept + diagram + terminology.

✅ 16. Quick Summary

  • Argument = Premise → Conclusion.

  • Deductive = certainty; Inductive = probability.

  • Categorical logic: A, E, I, O + Square of Opposition.

  • Fallacies: Formal & Informal.

  • Language: Connotation/Denotation influence meaning.

  • Venn Diagrams: visual validity tests.

  • Indian Logic: 6 Pramāṇas, Anumāna structure, Hetvābhāsa types.

👋Subscribe to
ProTeacher.in

Sign up to receive NewsLetters in your inbox.

We don’t spam! Read our privacy policy for more info.