Reasoning

Syllogism, Inequality & Statement-Conclusion

Syllogism, coded inequality and statement-conclusion are deduction-based questions that test whether you can derive a definite conclusion from given premises. They are easy 4–6 marks once you master the standard rules and Venn-diagram method.

Exam relevance: Banking exams (IBPS, SBI, RBI): 5 syllogism + 5 inequality questions in Prelims. SSC CGL: 2–3 statement-conclusion. State PSC: 3–5 questions.

In-Depth Tutorial

A formal, accessible 800–1000 word walkthrough of this topic, written for the serious aspirant. Switch to हिन्दी using the toggle on the right.

Why Logic-Based Reasoning Is the Most Predictable Score-Booster

Syllogism, statement-and-conclusion, statement-and-assumption, and inequality questions form the formal-logic family of reasoning. Unlike puzzles, which require minutes of construction, a logic question is rule-bound: once the candidate has internalised the rules of valid inference, every question in the family becomes a near-mechanical application. This predictability is precisely why these questions consistently appear in the Staff Selection Commission, the Institute of Banking Personnel Selection, the Reserve Bank of India recruitment, the State Public Service Commissions, and the preliminary papers of the Combined Defence Services and the Civil Services.

An aspirant who has spent ten focused hours on this family can typically solve a five-question syllogism set in three minutes and a five-question inequality set in two minutes — eight to ten near-certain marks per paper. There is no other topic in reasoning where the time-to-mark ratio is as favourable.

Syllogism — The Logic of All, Some and No

A syllogism question presents two or three statements such as 'All cats are mammals; All mammals are animals' and asks the candidate to determine which conclusions definitely follow. Four standard statement types exist: universal affirmative ('All A are B'), universal negative ('No A are B'), particular affirmative ('Some A are B') and particular negative ('Some A are not B'). The candidate must learn the eight valid combinations of two premises and the conclusions each combination yields.

The Venn-diagram method is the most reliable in the examination hall. The candidate draws a possibility diagram for each premise, then checks each conclusion against every possible diagram. A conclusion follows only if it is true in every possibility, not merely in one. This single discipline — testing across all possibilities — converts the trickiest syllogism into a mechanical task. The two famous extensions, 'either-or' and 'possibility' conclusions, are then specific cases of this general method.

Statement and Conclusion — Reading Without Adding

Statement-and-conclusion questions present a short paragraph and a list of conclusions, asking which conclusions definitely follow from the statement alone. The single most important rule is to never bring in outside knowledge. If the statement says, 'The government has reduced petrol prices,' the candidate cannot conclude that inflation will fall; that conclusion may be true in real life but is not stated. The conclusion must be derivable strictly from the words on the page.

The professional method is to underline the key claim of the statement, then read each conclusion and ask only one question: does the statement, taken at face value, force this conclusion? If even one alternative interpretation of the statement allows the conclusion to be false, the conclusion does not follow. This strictness is what distinguishes a candidate who scores three out of five from a candidate who scores five out of five.

Statement and Assumption — The Implicit Foundation

An assumption is a fact that must be true for the statement to make sense, even if it is not explicitly stated. For instance, the statement 'Please carry an umbrella when you leave the house' assumes that it may rain or that the sun may be intense. The candidate's task is to determine whether the listed assumption is implicit in the statement.

Two reliable tests are used. First, the negation test — if negating the assumption makes the statement collapse into nonsense, the assumption is implicit. Second, the necessity test — if the action recommended in the statement would still make sense without the assumption, the assumption is not implicit. Applying both tests in succession resolves almost every borderline case in this sub-topic, including the deliberately confusing examples that examiners include to separate average from excellent candidates.

Inequality — Symbol Translation Made Simple

Inequality questions present sequences of symbols such as A > B ≥ C < D and ask which conclusions hold. The professional method is a two-step translation. First, simplify the chain so that each pair of consecutive variables is connected by a single direction-aware relation. Second, evaluate each conclusion against the simplified chain.

Three rules govern conclusions. First, a strict inequality combined with another strict inequality of the same direction yields a strict inequality. Second, a strict inequality combined with a non-strict inequality (≥ or ≤) of the same direction yields a strict inequality. Third, two non-strict inequalities of the same direction yield a non-strict inequality. Mixing directions blocks any conclusion entirely. Coded inequality, where symbols such as @, # and $ replace the standard signs, is solved by writing a two-line key at the top of the rough sheet and treating the question as a routine inequality thereafter.

A Two-Week Mastery Plan

An efficient plan covers the entire logic family in two weeks. The first week treats syllogism and inequality, with twenty syllogism questions and twenty inequality questions per day, every question solved with a Venn diagram or a translated chain even when the answer feels obvious. This drill builds the habit of writing the diagram first and answering only afterwards.

The second week treats statement-conclusion and statement-assumption, with fifteen questions of each per day, focusing on the negation and necessity tests. By the end of the fortnight, the candidate is capable of solving any logic-family set in under five minutes with ninety-five-percent accuracy. These eight to ten reliable marks then form the high-confidence anchor that allows the candidate to spend more time on the harder puzzle sets in the same paper.

1Syllogism (All / Some / No / Some-Not)

Syllogism gives two or more premises and asks which of the given conclusions logically follows.

Use the Venn-diagram method. Draw circles for each subject and apply the premise: 'All A are B' → A is fully inside B; 'Some A are B' → A and B overlap; 'No A is B' → A and B are disjoint; 'Some A are not B' → at least part of A lies outside B. Apply the 'possibility' rule when the conclusion contains 'may be' or 'possibility'. Standard rules: 'all + all = all', 'all + no = no', 'some + all = some', 'some + no = some-not', and 'no + no = no conclusion'.

Examples
  • All cats are mammals. All mammals are animals. → All cats are animals (definite).
  • Some pens are pencils. All pencils are erasers. → Some pens are erasers (definite); Some erasers are pens (definite).
  • No bird is a fish. All fish are aquatic. → No bird is a fish (premise); No conclusion that all aquatic are non-birds.
  • All flowers are red. Some red are blue. → No definite conclusion (middle term not distributed).
Exam tip: If the middle term is not distributed in at least one premise, no definite conclusion can be drawn. Use Venn diagrams whenever statements feel ambiguous.

2Coded Inequality (Direct & Indirect)

Coded inequality replaces standard symbols (>, <, =, ≥, ≤) with codes like @, $, # and asks which conclusion follows.

Step 1: decode each symbol from the legend. Step 2: rewrite the premises using standard inequality signs. Step 3: link the inequalities through a common term. A conclusion follows ONLY if the chain of inequalities supports it AND the inequality types are compatible. '>=' combined with '>' gives '>'; '>' combined with '=' gives '>'; '>' combined with '<' gives NO definite conclusion.

Examples
  • If A > B, B = C → A > C (definite).
  • If A ≥ B, B > C → A > C (definite, strict).
  • If A > B, B < C → no relation between A and C.
  • If A = B, B ≥ C → A ≥ C (definite).
Exam tip: When a chain breaks at an unequal sign (e.g. A > B < C), no relation between A and C can be established. Check each pair individually.

3Statement & Conclusion / Course of Action

A statement is given, followed by 2–3 conclusions or courses of action. You must decide which logically follow or which are reasonable steps.

For 'conclusion follows': it must be DIRECTLY implied by the statement — no extra assumption allowed. For 'course of action': the action must be PRACTICAL, FEASIBLE and address the problem stated. Reject impractical, vague or extreme actions even if they sound positive. Always re-read the conclusion against the statement word-by-word.

Examples
  • Statement: 'Smoking is injurious to health.' Conclusion: 'People should avoid smoking.' → Follows.
  • Statement: 'Rain caused traffic jams.' Course of action: 'All vehicles should be banned.' → Does not follow (extreme).
  • Statement: 'Petrol prices have risen.' Conclusion: 'Public transport should be encouraged.' → Follows (logical action).
  • Statement: 'X scored highest in the exam.' Conclusion: 'X is the most intelligent in class.' → Does not follow (intelligence ≠ exam score).
Exam tip: Reject conclusions that require extra information not in the statement. The phrase 'should' usually triggers a course-of-action question — verify feasibility, not just intent.

Short Tricks & Shortcuts

Use these speed tricks in the exam. Each trick is followed by a worked example so you can verify the shortcut yourself.

Trick 1Venn-diagram method for syllogism

Draw circles for each subject. 'All A are B' → A inside B. 'Some A are B' → A & B overlap. 'No A is B' → disjoint. The conclusion follows ONLY if it is true in EVERY possible Venn diagram.

Example: All cats are mammals; all mammals are animals → cats are inside animals → 'All cats are animals' follows.
Trick 2Possibility-conclusion rule

If the conclusion contains 'may be', 'possibility' or 'can be', it is true if AT LEAST ONE valid Venn diagram supports it. (For 'definite' conclusions, ALL diagrams must support it.)

Example: Some A are B → 'Some A are not B' is a POSSIBILITY (overlap could be partial).
Trick 3Inequality chain compatibility

'>' + '=' = '>'. '≥' + '>' = '>'. '>' + '<' = NO conclusion. '=' + '=' = '=' . The chain breaks at any direction reversal.

Example: A > B = C → A > C; A > B < C → no relation.
Trick 4Either-or rule for syllogism

When two conclusions are individually 'not following' but together cover all possibilities (one overlap, one no-overlap), the answer is 'Either I or II follows'. Both subjects must be the same.

Example: 'Some A are B' / 'No A is B' on the same pair → Either I or II follows.
Trick 5Course-of-action feasibility check

Three filters: (1) Is the action directly addressing the problem? (2) Is it practical and proportionate? (3) Is it within authority? If any fails, the action does NOT follow.

Example: Statement: petrol shortage. Action: ban all vehicles → fails feasibility & proportion → does not follow.

Quick Revision Facts

  • All + All = All. All + No = No. Some + All = Some. No + No = No definite conclusion.
  • If the middle term is undistributed in both premises, no conclusion can be drawn.
  • An 'either-or' conclusion is valid only when both options share the same subject and predicate.
  • Inequality chains break at sign reversals (>< or <>).

Frequently Asked Questions

When two conclusions for the same pair of subjects are individually 'not following' but together exhaust all possibilities — typically one says 'some are' and the other 'none is'. Then mark 'Either I or II follows'.

Three checks: (1) does it address the problem stated? (2) is it practical/feasible? (3) is it proportionate? If any answer is no, the action does NOT follow.