Deduction
A conclusion is accepted only when it necessarily follows from the premises.
Note 23
Logical Deduction and Inference
Complete notes for SSC Combined Graduate Level examinations
1The Big Picture — Graphic Mind Map
Syllogism
Class relations expressed through all, no and some statements.
Conclusion
Test relevance and necessity; never add outside facts or expectations.
Assumption
An unstated idea the statement needs or takes for granted.
Argument
Strong arguments are relevant, substantial, practical and logically connected.
Cause–Effect
Cause precedes and plausibly produces the effect; sequence alone is insufficient.
Decision Table
Apply stated conditions mechanically; reject options violating any mandatory rule.
Critical Thinking
Separate evidence from claim, fact from opinion, and possibility from certainty.
1. Isolate
premises
➜premises
2. Formalise
relations
➜relations
3. Test
necessity
➜necessity
4. Challenge
counterexample
➜counterexample
5. Decide
only what follows
only what follows
2The Foundation — From Premises to Valid Decisions
2.1 Core Vocabulary
- Premise: a supplied statement accepted for the question.
- Inference: a proposition derived from premises.
- Conclusion: the claim tested as following from them.
- Validity: impossible for premises to be true and conclusion false.
- Truth: correspondence with reality—different from validity.
2.2 Certainty Ladder
Must follow means every permitted situation supports it. May follow needs only one permitted situation. Cannot follow conflicts with every permitted situation.
SSC conclusion questions normally test necessity, not probability or plausibility.
2.3 Validity vs Soundness
| Concept | Question | Depends on | Example insight |
|---|---|---|---|
| Valid argument | If premises were true, must conclusion follow? | Logical form | Can contain factually false premises |
| Sound argument | Is it valid with true premises? | Form plus truth | Guarantees true conclusion |
| Strong inductive support | Do premises make conclusion likely? | Evidence quality and representativeness | Does not give certainty |
| Consistency | Can all statements be true together? | Absence of contradiction | Consistent statements need not prove one another |
2.4 Categorical Syllogisms — Four Forms
A: All \(S\) are \(P\)
\[S\subseteq P\]
The entire subject class lies inside the predicate class.
E: No \(S\) is \(P\)
\[S\cap P=\varnothing\]
The classes are disjoint.
I: Some \(S\) are \(P\)
\[S\cap P\ne\varnothing\]
At least one object belongs to both.
O: Some \(S\) are not \(P\)
\[S\setminus P\ne\varnothing\]
At least one subject lies outside the predicate.
2.5 Conversion, Opposition and Existential Caution
| Statement | Safe immediate inference | Unsafe inference | Reason |
|---|---|---|---|
| All \(A\) are \(B\) | Some \(B\) are \(A\), only if existence of \(A\) is established | All \(B\) are \(A\) | Subset is not equality |
| No \(A\) is \(B\) | No \(B\) is \(A\) | Some \(A\) are not \(B\) without existence | Disjointness converts; existence may not |
| Some \(A\) are \(B\) | Some \(B\) are \(A\) | All \(A\) are \(B\) | Intersection is symmetric but partial |
| Some \(A\) are not \(B\) | No simple conversion | Some \(B\) are not \(A\) | Witness belongs to \(A\), not necessarily \(B\) |
2.6 Chain Inclusion
If all \(A\) are \(B\), and all \(B\) are \(C\), then all \(A\) are \(C\):
\[A\subseteq B,\ B\subseteq C\implies A\subseteq C\]
2.7 Particular Witness
“Some” creates at least one witness. Track where that witness must and may lie; never turn it into a whole-class rule.
If some \(A\) are \(B\) and all \(B\) are \(C\), then some \(A\) are \(C\).
2.8 Negative Chain
If all \(A\) are \(B\) and no \(B\) is \(C\), then no \(A\) is \(C\).
\[A\subseteq B,\ B\cap C=\varnothing\implies A\cap C=\varnothing\]
2.9 Statement–Conclusion Method
Necessity test
- Use only the statement.
- Translate universal words precisely.
- Try to make premises true and conclusion false.
- If any such counterexample exists, conclusion does not follow.
Language force
- All/every: universal.
- Some/at least one: existential.
- Only: reverses the direction candidates often assume.
- Unless: introduces an exception/condition.
- May/can: possibility, not certainty.
2.10 Statement–Assumption
Definition
An assumption is an unstated proposition accepted for the statement, proposal or action to make sense.
Negation test
Negate the proposed assumption. If the statement becomes pointless, incoherent or impossible to support, the assumption is implicit.
Guardrail
Necessary background support counts; a desirable result, moral approval or broad prediction need not be assumed.
2.11 Statement–Argument
| Strong argument | Weak argument | Diagnostic question |
|---|---|---|
| Directly addresses the issue | Changes topic or attacks a person | Is it relevant? |
| Uses significant, credible reasons | Uses slogans, emotion or isolated anecdotes | Is the support substantial? |
| Is practicable and considers consequences | Is vague, extreme or impossible | Can it work? |
| Respects the exact proposal | Distorts it into a stronger/weaker claim | Is it a straw man? |
2.12 Course of Action
Problem–remedy link
The action must address the stated problem or its cause, not merely express concern.
Practicality & proportionality
It should be implementable, lawful, proportionate and not create a worse problem.
Information sufficiency
Do not prescribe a specific action when essential facts are missing; inquiry/data collection may be the proper first step.
2.13 Cause and Effect
Minimum causal conditions
- Cause precedes effect.
- A plausible mechanism connects them.
- The cause has enough scope to produce the effect.
- No statement reverses direction or names a common cause.
Four possibilities
\(A\) causes \(B\); \(B\) causes \(A\); both share cause \(C\); or they merely coexist. Temporal sequence alone proves none.
2.14 Consistency, Contradiction and Equivalence
| Relation | Meaning | Quick test |
|---|---|---|
| Contradiction | Cannot both be true and cannot both be false in the same respect | \(P\) and \(\neg P\) |
| Contrary | Cannot both be true but may both be false | “All” versus “No” for existing mixed cases |
| Compatible | Can be true together | Construct one shared scenario |
| Equivalent | Same truth conditions | Each implies the other |
| Independent | Neither establishes nor rules out the other | Build all truth combinations |
2.15 Decision Tables & Judgment
Mechanical procedure
- Turn every condition into a column.
- Mark pass/fail/unknown.
- Apply mandatory disqualifiers first.
- Use exceptions only where their triggers hold.
- Select the prescribed action or authority.
Condition language
- Must: mandatory.
- May: permission, not requirement.
- Only if: necessary condition.
- If: sufficient condition.
- Unless: exception/default trigger.
2.16 Critical-Thinking Quality Check
Source
Expertise, proximity, independence, incentives and corroboration.
Evidence
Size, representativeness, controls, recency and directness.
Reasoning
Relevance, causal link, missing alternatives and consistency.
Claim
Scope, certainty, definition, exceptions and whether language overreaches evidence.
3Short Tricks & Magic Frameworks
3.1 All = Put Inside
“All \(A\) are \(B\)” means \(A\subseteq B\). Never reverse the container.
3.2 No = Keep Apart
Disjointness is symmetric: no \(A\) is \(B\) also means no \(B\) is \(A\).
3.3 Some = Place a Dot
One definite witness is enough. Carry the same dot through every forced class relation.
3.4 Counterexample Kill
To reject “must follow,” imagine one valid arrangement where premises hold but conclusion fails.
3.5 Negate Assumptions
If negation destroys the statement’s purpose or logic, the assumption is implicit.
3.6 RSP Argument Test
Relevant, Substantial, Practical. A strong argument clears all three.
3.7 P-M-A Course Test
Does it fit the Problem, use a valid Means, and produce an acceptable After-effect?
3.8 Causal Triangle
Check direction \(A\to B\), reverse \(B\to A\), and common cause \(C\to A,B\).
3.9 Disqualifier First
In decision tables, one failed mandatory condition may eliminate a case before other calculations.
3.10 Arrow Language
“\(A\) only if \(B\)” means \(A\implies B\); “\(A\) if \(B\)” means \(B\implies A\).
3.11 Fact–Opinion Split
Mark observable claims separately from judgments, preferences and predictions.
3.12 Scope Match
A conclusion cannot be broader, more certain or more causal than its evidence.
3.13 Compact Inference Bank
| Pattern | Safe result | Never jump to |
|---|---|---|
| \(A\subseteq B\), \(B\subseteq C\) | \(A\subseteq C\) | \(C\subseteq A\) |
| \(A\subseteq B\), \(B\cap C=\varnothing\) | \(A\cap C=\varnothing\) | \(B\subseteq A\) |
| Some \(A\) are \(B\), \(B\subseteq C\) | Some \(A\) are \(C\) | All \(A\) are \(C\) |
| No \(A\) is \(B\) | No \(B\) is \(A\) | Existence of either class |
| \(P\implies Q\) | \(\neg Q\implies\neg P\) | \(Q\implies P\) |
| Correlation | Association | Causation |
4The SSC / TCS Traps — Red Flags
🚩 4.1 Outside Knowledge
Premises control the reasoning—even when real-world facts suggest another answer.
🚩 4.2 Reversing “All”
\(A\subseteq B\) does not establish \(B\subseteq A\).
🚩 4.3 Some Becomes All
One witness cannot justify a universal conclusion.
🚩 4.4 Existential Import
Universal statements do not always guarantee that their subject class exists.
🚩 4.5 Restatement as Conclusion
A conclusion may paraphrase a premise validly, but a merely related slogan need not follow.
🚩 4.6 Desirable Assumption
What would be helpful or morally good is not necessarily what the statement assumes.
🚩 4.7 Emotional Argument
Strong feeling, popularity or authority does not replace relevant evidence.
🚩 4.8 Extreme Course
An action can address the issue yet fail because it is disproportionate, unlawful or impractical.
🚩 4.9 Correlation = Cause
Two events moving together may share a cause or be coincidental.
🚩 4.10 If / Only If
Confusing sufficient and necessary conditions reverses the decision rule.
🚩 4.11 Ignoring an Exception
Decision-table exceptions apply only when their full trigger conditions are met.
🚩 4.12 Scope Inflation
“Some,” “may,” or one study cannot support “all,” “will,” or universal causation.
Final red flag: plausible is not compulsory. Choose a conclusion only when every permitted interpretation of the premises supports it.
5Memory Hooks & Mnemonics
5.1 “FORCE” Inference
Facts only, Organise, Relate, Counterexample, Evaluate.
5.2 “All Goes Inside”
The subject circle goes completely inside the predicate circle.
5.3 “Some Needs a Dot”
A definite dot represents the existential witness; never spread it to the whole circle.
5.4 “Assumption Hates NOT”
Negate it: if the statement collapses, the hidden support was necessary.
5.5 “Arguments Need RSP”
Relevant, substantial and practical beats emotional or decorative reasoning.
5.6 “Action Must Touch Problem”
If the proposed remedy never touches the problem or cause, reject it.
5.7 “Look for the Third Guest”
When two events correlate, a hidden common cause may be visiting both.
5.8 “Table Before Judgment”
Turn prose conditions into columns; evidence beats intuition.
Deduction Recall
- Use premises only.
- Draw all/no/some precisely.
- Carry existential witnesses.
- Test a counterexample.
- Accept only necessary conclusions.
Critical Judgment Recall
- Negate assumptions.
- Test argument relevance and weight.
- Match action to problem.
- Challenge causal direction.
- Apply every decision condition.
Final recall line: “Facts first, necessity over plausibility, and no conclusion wider than its evidence.”