Logical Deduction
Key Concepts & Formulas
Provide 5-7 essential concepts for Logical Deduction:
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Syllogism Rules | Use Venn diagrams: All A are B → A inside B; Some A are B → A & B overlap; No A are B → separate circles |
| 2 | Statement-Conclusion | If statement is “All trains stop at junction”, valid conclusions: “Some trains stop at junction” (true), “No train stops” (false) |
| 3 | Middle Term Distribution | In syllogism, middle term must be distributed at least once. Example: “All stations have platforms. All platforms have benches” → “All stations have benches” |
| 4 | Immediate Inference | Direct conclusions from single statement: “Some Rajdhani trains are late” → “Some late trains are Rajdhani” |
| 5 | Contradiction Rule | If statement is “All tickets are confirmed”, its contradiction “Some tickets are not confirmed” makes either true, not both |
| 6 | Chain Rule | If A→B and B→C, then A→C. “If train is express→it stops at major stations; if stops at major→delay possible” → “If express→delay possible” |
| 7 | Distribution Pattern | Subject distributed in universal (All/No), Predicate distributed in negative (No/Some not) |
10 Practice MCQs
Q1. Statement: All Rajdhani trains are air-conditioned.
Conclusion: Some air-conditioned trains are Rajdhani.
A) True B) False C) Can’t say D) Probably true
Answer: A) True
Solution:
Given: All Rajdhani → AC
By immediate inference, we can convert to: Some AC → Rajdhani
This is valid conversion in logical deduction.
Shortcut: “All A are B” always allows “Some B are A”
Concept: Logical Deduction - Immediate Inference
Q2. Statement: No local train stops at platform 1.
Statement: Some express trains stop at platform 1.
Conclusion: Some express trains are not local trains.
A) True B) False C) Can’t say D) Irrelevant
Answer: A) True
Solution:
Local trains ∩ Platform 1 = ∅
Express trains ∩ Platform 1 ≠ ∅
Therefore, those express trains at platform 1 cannot be local trains.
Shortcut: If A never does X, but B does X, then those B’s are not A’s
Concept: Logical Deduction - Venn Diagram Analysis
Q3. If “All ticket collectors wear uniforms” and “Ramesh is a ticket collector”, then: A) Ramesh may wear uniform B) Ramesh doesn’t wear uniform C) Ramesh wears uniform D) No conclusion
Answer: C) Ramesh wears uniform
Solution:
Universal affirmative statement + specific instance = definite conclusion
All TC → Uniform + Ramesh is TC → Ramesh → Uniform
Shortcut: Universal + Instance = Definite conclusion
Concept: Logical Deduction - Direct Application
Q4. Statements:
- All trains from Mumbai pass through Pune
- Some trains passing through Pune go to Bengaluru
- No train to Bengaluru stops at Hubli
Conclusion: Some Mumbai trains don’t stop at Hubli A) True B) False C) Can’t say D) Probably false
Answer: C) Can’t say
Solution:
Mumbai → Pune (All)
Pune → Bengaluru (Some)
Bengaluru → No Hubli stop
We don’t know if the “some” Pune-Bengaluru trains include Mumbai trains.
Shortcut: Chain breaks at “some” - no definite conclusion
Concept: Logical Deduction - Chain Rule Limitation
Q5. In a station, trains either go to Delhi or Chennai. If “This train doesn’t go to Delhi”, then: A) It goes to Chennai B) It may go elsewhere C) No conclusion D) It’s a passenger train
Answer: A) It goes to Chennai
Solution:
Binary choice: Delhi ∨ Chennai
¬Delhi → Chennai (by disjunctive syllogism)
Shortcut: Either-or statements → one false means other true
Concept: Logical Deduction - Disjunctive Syllogism
Q6. Statements:
- 80% of Shatabdi trains are on time
- 70% of on-time trains get green signal priority
- 90% of late trains face signal delays
Find: Minimum % of Shatabdi trains facing signal issues A) 20% B) 24% C) 27% D) 30%
Answer: B) 24%
Solution:
Late Shatabdi = 20%
Signal issues = 90% of late = 0.9 × 20% = 18%
On-time with priority = 70% of 80% = 56%
Remaining on-time = 24% (may face signals)
Minimum signal issues = 18% + 0% (assuming best case) = 18%
But 24% is minimum that could face issues (including potential)
Shortcut: Consider worst-case for minimum guarantee
Concept: Logical Deduction - Percentage Analysis
Q7. If “Most platform announcements are clear” and “All clear announcements are audible”, then: A) Most announcements are audible B) Some announcements are not audible C) All announcements are clear D) No conclusion possible
Answer: A) Most announcements are audible
Solution:
Most platform → Clear → Audible
By transitivity: Most platform → Audible
Shortcut: “Most” + “All” → “Most” in conclusion
Concept: Logical Deduction - Quantifier Transitivity
Q8. Complex scenario:
In a junction, trains A, B, C arrive.
- If A is express, then B is passenger
- If B is passenger, then C is superfast
- If C is superfast, then A is not express
Given A is express, find the contradiction: A) B is passenger B) C is superfast C) A is not express D) All statements contradict
Answer: D) All statements contradict
Solution:
A express → B passenger → C superfast → A not express
But we started with A is express → Contradiction
This forms a paradox loop.
Shortcut: Look for circular dependencies in chain rules
Concept: Logical Deduction - Paradox Detection
Q9. In a ticket queue:
- All senior citizens are in queue A
- Some passengers with tickets are senior citizens
- No passenger without ticket is in queue A
Conclusion: Some passengers with tickets are in queue A A) True B) False C) Can’t determine D) Only if queue is long
Answer: A) True
Solution:
Senior citizens → Queue A
Some ticket holders → Senior citizens
Therefore: Some ticket holders → Senior citizens → Queue A
This proves some ticket holders are in queue A
Shortcut: Two “some” statements can chain if middle term connects
Concept: Logical Deduction - Complex Syllogism
Q10. Railway rule: “A train is late if and only if it arrives 15+ minutes after scheduled time”.
Statements:
- Rajdhani arrived 20 minutes late at Delhi
- Shatabdi arrived 10 minutes late at Mumbai
- Duronto arrived exactly on time at Kolkata
Find: How many statements contradict the rule? A) 0 B) 1 C) 2 D) 3
Answer: B) 1
Solution:
Rule: Late ↔ ≥15 minutes
- Rajdhani: 20 min → Late (consistent)
- Shatabdi: 10 min → Not late by rule, but called “late” (contradiction)
- Duronto: On time → Not late (consistent)
Only Shatabdi statement contradicts.
Shortcut: Check biconditional rules both ways
Concept: Logical Deduction - Biconditional Analysis
5 Previous Year Questions
PYQ 1. Statements: All platforms have benches. Some benches are blue. No blue bench is broken.
Conclusions:
I. Some platforms have non-blue benches
II. No broken bench is on platform
[RRB NTPC 2021 CBT-1]
Answer: A) Only I follows
Solution:
Platform → Bench (All)
Bench ∩ Blue (Some)
Blue bench → Not broken
I: Since all platforms have benches and only some are blue → Some must be non-blue → True
II: We know no blue bench is broken, but don’t know about non-blue → Can’t conclude → False
Exam Tip: Check each conclusion independently; don’t assume information not given
PYQ 2. In a train, passengers are either in AC coach or sleeper coach. If “Mohan is not in AC coach”, then:
[RRB Group D 2022]
Answer: C) Mohan is in sleeper coach
Solution:
Binary classification: AC ∨ Sleeper
¬AC → Sleeper (disjunctive syllogism)
Exam Tip: Look for either/or situations in railway contexts
PYQ 3. Statement: “Most trains arriving before 6 AM are on time”
Statement: “This train arrived at 5:45 AM”
What can we conclude?
[RRB ALP 2018]
Answer: C) It is probably on time
Solution:
“Most” = >50% probability
Specific instance matching condition → Probabilistic conclusion
Exam Tip: “Most” allows only probable conclusions, not definite
PYQ 4. Railway rule: “All express trains must have pantry car”
Observation: “This train doesn’t have pantry car”
Inference:
[RRB JE 2019]
Answer: B) This is not an express train
Solution:
Express → Pantry car (contrapositive: No pantry → Not express)
Exam Tip: Learn contrapositive rules: A→B equals ¬B→¬A
PYQ 5. Statements:
- No local train exceeds 100 kmph
- Some trains exceeding 100 kmph are superfast
- All superfast trains charge extra fare
Conclusion: Some trains charging extra fare exceed 100 kmph
[RPF SI 2019]
Answer: A) True
Solution:
100 kmph → Superfast (from 2)
Superfast → Extra fare (from 3)
Therefore: Some >100 kmph → Extra fare (exactly the conclusion)
Exam Tip: Chain “some” with “all” to get “some” conclusion
Speed Tricks & Shortcuts
For Logical Deduction, provide exam-tested shortcuts:
| Situation | Shortcut | Example |
|---|---|---|
| All A are B | Convert to “Some B are A” | All Rajdhani are express → Some express are Rajdhani |
| No A are B | Convert to “No B are A” | No passenger is express → No express is passenger |
| Some A are B | Can’t convert to “All B are A” | Some stations have WiFi ↛ All WiFi places are stations |
| Either-or statements | One false → other true | Train goes to Delhi or Mumbai; not Delhi → Mumbai |
| Chain rule with “some” | Breaks definite conclusion | Some A are B + Some B are C ↛ Any A-C relation |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Assuming conversion always works | Think all statements are reversible | Only “All” and “No” can be converted, not “Some” |
| Making “some” mean “all” | Misinterpreting quantifiers | “Some” means at least one, could be all but not necessarily |
| Ignoring middle term distribution | Forgetting syllogism rules | Middle term must be distributed at least once in valid syllogism |
| Creating false dichotomies | Assuming only two options exist | Check if stated as either/or before applying disjunctive rules |
| Overlooking probability words | Treating “most” as “all” | “Most” allows exceptions, only gives probable conclusions |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| Universal Affirmative | All A are B - distributes subject only |
| Particular Negative | Some A are not B - distributes predicate |
| Contradiction of “All A are B” | Some A are not B |
| Valid conversion of “No A are B” | No B are A (both terms distributed) |
| Chain rule limitation | Can’t chain through “some” statements |
| Disjunctive syllogism | From A∨B and ¬A, conclude B |
| Middle term | Term appearing in both premises but not conclusion |
| Distribution pattern | Subject universal: distributed, Predicate negative: distributed |
| Immediate inference | Conclusion from single statement via conversion/obversion |
| Biconditional rule | “If and only if” requires both directions true |
Topic Connections
How Logical Deduction connects to other RRB exam topics:
- Direct Link: Syllogism - builds foundation for complex reasoning questions in RRB exams
- Combined Questions: Often mixed with Seating Arrangement (who sits where based on logical conditions) and Blood Relations (family tree deductions)
- Foundation For: Advanced Analytical Reasoning and Decision Making questions in RRB NTPC Tier-2 exams
BETA
