Chapter 29
Syllogisms, Analogies & Logical Deduction
All A are B; some B are C — what follows? Venn-diagram method.
Full Chapter Notes
Source · FPSC Trap Decoder · CSS MPT Smart Notes (2026 Edition)
High-Yield Snapshot
| Attribute | Value |
|---|---|
| MPT Weightage | 3–5 Marks |
| Difficulty | Medium |
| Problem Types Confirmed | 6 types across 4 past papers |
Logical deduction questions are among the most consistently failed questions in the entire MPT — not because they are mathematically hard, but because candidates approach them using common sense and personal knowledge rather than formal logic.
FPSC Trap — The Fundamental Error: Using Real-World Knowledge. A candidate who applies real-world knowledge ("all politicians are corrupt") to a logic question will fail it. A candidate who treats the given statements as the only truth in the universe and reasons mechanically from them will score full marks.
Concept Anchor — The Supreme Rule
The statements given are assumed to be 100% true, even if they contradict reality. If the question says "All cats are dogs," accept it as true for the purpose of solving that question. Then ask:
- What MUST logically follow from this truth?
- What MIGHT follow?
- What definitely does NOT follow?
The moment you bring in outside knowledge — "but cats aren't dogs in real life" — you have left the world of logic. Common sense fails logic questions. Mechanical deduction wins them.
The Six Problem Types
Type 1 — Syllogisms (All, Some, No)
A syllogism gives you two statements (premises) and asks what conclusion must follow.
| Quantifier | Meaning | Example |
|---|---|---|
| All | Every single member without exception | All birds can fly |
| Some | At least one, possibly all | Some birds are white |
| No | Not a single member | No fish are mammals |
Pattern 1 — All + All = All: If all A are B, and all B are C, then all A are C. Example: All dogs are animals. All animals are living things. → All dogs are living things.
Pattern 2 — All + No = No: If all A are B, and no B are C, then no A are C. Example: All roses are flowers. No flowers are stones. → No roses are stones.
Pattern 3 — Some + All = Some: If some A are B, and all B are C, then some A are C. Example: Some students are athletes. All athletes are disciplined. → Some students are disciplined.
Pattern 4 — All + Some (CRITICAL TRAP): If all A are B, and some B are C — you CANNOT conclude that some A are C. The "some B" might be entirely from the non-A part of B.
| Premise 1 | Premise 2 | Valid Conclusion |
|---|---|---|
| All A are B | All B are C | All A are C (certain) |
| Some A are B | All B are C | Some A are C (certain) |
| All A are B | No B are C | No A are C (certain) |
| Some A are B | Some B are C | Nothing certain — no valid conclusion |
| Some A are B | No B are C | Some A are not C (certain) |
Diagram recommended here to illustrate Venn diagram representations of each syllogism pattern.
Type 2 — Statement and Conclusion
The question gives one or two factual statements and asks which of the given conclusions logically follows.
- Read the statement carefully — accept it as absolute truth.
- For each conclusion, ask: does this HAVE to be true if the statement is true?
- If yes → conclusion follows.
- If maybe / sometimes / depends → conclusion does NOT follow.
- If the conclusion requires outside information not given in the statement → does NOT follow.
Confirmed FPSC Example (CSS MPT 2023 Special Q110):
"Some candies in the pack are lemon-flavoured. Some candies in the pack are blue-coloured." Which conclusion follows?
- (A) Some candies are lemon-flavoured.
- (B) All lemon-flavoured candies are blue-coloured.
- (C) All candies are blue-coloured.
- (D) None of these.
FPSC Trap — Restatement is NOT a Valid Conclusion. Option A is an exact restatement of the first premise. In formal syllogism testing, a conclusion that simply restates a premise is not considered a valid logical deduction — it is a tautology. A conclusion must add NEW information derived logically from the premises. Option B: Cannot conclude — we only know SOME of each colour, not their overlap. Option C: Clearly does not follow from "some are blue." Correct answer: D — None of these.
Type 3 — Cause and Effect / Logical Sequence
The question describes a situation and asks what logically comes next, what caused it, or what would remedy it.
- Identify what is described (a problem, a change, a situation).
- Find the option that is the direct, necessary, logical consequence — not a possible one, not a related one.
- Eliminate options that require additional assumptions.
Example: "Vitamin C deficiency causes scurvy. Raza has scurvy." Which follows?
- (A) Raza should take Vitamin C supplements.
- (B) Raza does not eat vegetables.
- (C) Raza will die.
- (D) All patients with scurvy are malnourished.
Analysis:
- Option A: If scurvy is caused by Vitamin C deficiency, the logical remedy is Vitamin C. This follows.
- Option B: Requires assuming vegetables are the only source of Vitamin C. Does not logically follow.
- Option C: Requires assuming all cases of scurvy are fatal. Does not follow.
- Option D: Requires a broader generalisation not supported by the premise.
Answer: A.
Type 4 — Word Analogies (Extended)
Also covered in Chapter 32, but FPSC uses word analogies in the logical deduction section in a harder format — where the relationship itself must be identified before the answer can be found.
| Relationship Type | Example | How to Check |
|---|---|---|
| Cause : Effect | Fire : Smoke | Smoke does NOT cause Fire (direction matters) |
| Tool : Purpose | Pen : Write | Write is the purpose; Pen is the tool |
| Part : Whole | Chapter : Book | Chapter is part of Book |
| Worker : Workplace | Doctor : Hospital | Doctor works at Hospital |
| Item : Category | Rose : Flower | Rose IS a type of Flower |
| Action : Object | Teach : Student | Teach acts on Student |
| Degree / Intensity | Warm : Hot | Hot is the stronger degree |
| Opposite | Dark : Light | These are antonyms |
- State the relationship of the given pair in a complete sentence.
- Apply the EXACT SAME sentence structure to find the answer.
- Reject options where the relationship is similar but not identical.
Example: Library : Books :: Museum : ? → "A library contains books." → "A museum contains ___." → Exhibits / Artefacts.
Type 5 — Premise-Based Deduction (Logical Validity)
The question gives a set of statements and asks whether a specific argument is valid, invalid, or whether the conclusion necessarily follows.
- Valid argument: The conclusion MUST be true IF the premises are true. Validity is about logical structure, not truth.
- Sound argument: Valid AND the premises are actually true in the real world.
FPSC only tests validity — not soundness.
Example of a valid but unsound argument:
- Premise 1: All birds can fly.
- Premise 2: Penguins are birds.
- Conclusion: Penguins can fly.
This argument is valid (the conclusion logically follows from the premises) but unsound (Premise 1 is false in reality). In a logic question, if FPSC gives you these premises, the conclusion "penguins can fly" FOLLOWS — even though you know penguins cannot fly.
Diagram recommended here to illustrate the valid vs. unsound argument distinction.
Type 6 — Odd Statement Out (Logical Category)
The question gives four statements or word groups and asks which one does not belong.
- Identify what three of the four have in common.
- The fourth that breaks the pattern is the odd one out.
- The property must be logical/categorical — not based on spelling or sound.
Example: Judge, Lawyer, Doctor, Court → Judge, Lawyer, Court all relate to the legal system. Doctor → medical profession. Odd one out: Doctor.
CSSPrep Solved Examples
Problem:
- Premise 1: All politicians are leaders.
- Premise 2: All leaders are educated.
- Conclusion 1: All politicians are educated.
- Conclusion 2: All educated people are politicians.
Which conclusion(s) follow?
Step 1 — Identify the syllogism pattern. Premise 1: All A are B. Premise 2: All B are C. Pattern: All + All = All → All A are C.
Step 2 — Test Conclusion 1 ("All politicians are educated"). The pattern yields: All A (politicians) are C (educated). This matches the derived conclusion directly. Follows.
Step 3 — Test Conclusion 2 ("All educated people are politicians"). This reverses the direction of the chain: it claims All C are A. From "All A are C" one CANNOT conclude "All C are A". Being educated does not imply being a politician. Does not follow.
| Proposition | Symbolic Form | Result |
|---|---|---|
| All A are B + All B are C | A ⊆ B, B ⊆ C | All A are C ✓ |
| Reverse: All C are A? | C ⊇ A (invalid inference) | Does NOT follow ✗ |
Answer: Only Conclusion 1 follows.
Problem:
- Premise 1: Some doctors are scientists.
- Premise 2: All scientists are researchers.
- Conclusion 1: Some doctors are researchers.
- Conclusion 2: All doctors are researchers.
Which conclusion(s) follow?
Step 1 — Identify the syllogism pattern. Premise 1: Some A are B. Premise 2: All B are C. Pattern: Some + All = Some → Some A are C.
Step 2 — Test Conclusion 1 ("Some doctors are researchers"). Pattern yields: Some A (doctors) are C (researchers). This is exactly the derived result. Follows.
Step 3 — Test Conclusion 2 ("All doctors are researchers"). The pattern only guarantees "Some," never "All." Doctors who are not scientists have no established link to researchers. Upgrading "Some" to "All" is an invalid inference. Does not follow.
| Proposition | Symbolic Form | Result |
|---|---|---|
| Some A are B + All B are C | A ∩ B ≠ ∅, B ⊆ C | Some A are C ✓ |
| Can we conclude All A are C? | A ⊆ C (unverified) | Does NOT follow ✗ |
Answer: Only Conclusion 1 follows.
Problem:
- Premise 1: All smartphones are electronic devices.
- Premise 2: No electronic devices are animals.
- Conclusion: No smartphones are animals.
Step 1 — Pattern. Premise 1: All A are B. Premise 2: No B are C. Pattern: All + No = No → No A are C.
Step 2 — Test the Conclusion. Pattern yields: No A (smartphones) are C (animals). The conclusion matches exactly. Follows.
| Proposition | Symbolic Form | Result |
|---|---|---|
| All A are B + No B are C | A ⊆ B, B ∩ C = ∅ | No A are C ✓ |
Answer: The conclusion follows.
Problem:
- Statement 1: Some candies in the pack are lemon-flavoured.
- Statement 2: Some candies in the pack are blue-coloured.
Which of the following conclusions follows?
- (A) Some candies are lemon-flavoured.
- (B) All lemon-flavoured candies are blue-coloured.
- (C) All candies are blue-coloured.
- (D) None of these.
Step 1 — Test Option (A). This is a verbatim restatement of Statement 1. A valid conclusion must derive NEW information from the premises; a mere restatement is not a logical deduction. Eliminated.
Step 2 — Test Option (B). No information about any overlap between lemon-flavoured and blue-coloured subsets is given. The two "Some" statements are independent. Inferring "All lemon = blue" has no basis. Eliminated.
Step 3 — Test Option (C). Statement 2 says only SOME candies are blue. Upgrading "Some" to "All" is an invalid inference. Eliminated.
Answer: (D) None of these. Confirmed CSS MPT 2023 — Special Q110.
Problem 1: Pen : Write :: Camera : ? Problem 2: Book : Library :: Painting : ? — (A) Artist (B) Museum (C) Canvas (D) Colour
Problem 1 — Relationship: "A pen is used to write." → Tool → its specific function. "A camera is used to ___." → Photograph.
Problem 2 — Relationship: "A book is stored and publicly displayed in a library." → Object → the institution where it is kept and displayed. "A painting is stored and displayed in a ___." → Museum.
Eliminating distractors:
- (A) Artist — who creates it, not where it is kept.
- (C) Canvas — what it is painted on (material, not location).
- (D) Colour — a component, not a place.
- (B) Museum — the institution that displays paintings. ✓
Answer: Problem 1: Photograph. Problem 2: (B) Museum.
Problem: "Regular exercise reduces the risk of heart disease." Which conclusion logically follows?
- (A) People who exercise never get heart disease.
- (B) People who do not exercise will get heart disease.
- (C) Exercising regularly may help prevent heart disease.
- (D) Heart disease is only caused by lack of exercise.
Step 1 — Analyze the language. Key phrase: "…REDUCES THE RISK…" This means probability decreases — it does not eliminate risk, does not guarantee disease, and does not name a sole cause.
Step 2 — Test (A): "Never" = absolute elimination of risk. The statement only says "reduces." Too strong.
Step 3 — Test (B): "Will" = certainty. Reducing risk for one group does not guarantee disease for the other group. Too strong.
Step 4 — Test (C): "May help prevent" is perfectly consistent with "reduces the risk." No over-claim, no under-claim. Correct.
Step 5 — Test (D): The statement never mentions exercise as the sole cause. Introducing "only" goes far beyond the evidence. Too strong.
Answer: (C) Exercising regularly may help prevent heart disease.
Problem:
- All successful people wake up early.
- Sara wakes up early.
- Therefore, Sara is successful.
Is this argument logically valid?
Step 1 — Map the argument symbolically. Let A = successful people. Let B = people who wake up early.
- Premise 1: All A are B (all successful people wake up early)
- Premise 2: Sara ∈ B (Sara wakes up early)
- Conclusion: Sara ∈ A (Sara is successful)
Step 2 — Identify the logical flaw. From "All A ⊆ B" and "Sara ∈ B" one CANNOT conclude "Sara ∈ A". The set B may contain many members who are not in A. Non-successful people can also wake up early. The valid inference would require the converse: "All B ⊆ A" (all early risers are successful) — which was NOT given.
Verdict: This is affirming the consequent — a classic invalid argument.
Common Mistakes
| Mistake | Wrong Approach | Correct Approach |
|---|---|---|
| Reversing "All A are B" | "All dogs are animals" → "All animals are dogs" | "All A are B" reverses to only "Some B are A" — never "All B are A" |
| Using real-world knowledge | "All birds can fly — but penguins can't, so this is wrong" | Accept the premise as given truth. In this logical world, all birds fly. |
| "Some" treated as "Most" or "All" | "Some doctors are rich" → most doctors are rich | "Some" means at least one — possibly very few. Some = minimum 1. Could be all. |
| "Follows" confused with "Is true" | Checking if the conclusion is true in real life | Checking if the conclusion MUST follow from the given premises. |
| Restatement accepted as a conclusion | Premise: "Some X are Y." → Conclusion: "Some X are Y" — follows! | A restatement of the premise is NOT a logical conclusion. |
FPSC Trap Alert
Trap 1 — The Restatement Trap. When FPSC gives you conclusions, one will often be an exact or near-exact restatement of one of the premises. Many candidates pick this because it is "obviously true." A valid conclusion must derive NEW information — restating the premise is not valid deduction. The correct answer is often "None of these" when all given conclusions are either restatements or unjustified leaps. CSS MPT 2023 Special Q110 confirmed this.
Trap 2 — The Universal Reversal Trap. "All A are B" does NOT mean "All B are A." This reversal error is present in almost every FPSC syllogism question. Always ask: does the conclusion go from A to B (as stated) or does it reverse from B to A (not stated)? If it reverses — it does not follow.
Trap 3 — The "Some + Some = Something" Trap. When both premises use "Some," no definite conclusion is possible. "Some A are B" and "Some B are C" tells you NOTHING certain about the relationship between A and C. The "some B" in each premise might be completely different members of B. FPSC places plausible-sounding conclusions for this pattern — all of them are wrong. Answer is always "None of these."
Trap 4 — The "Reduces Risk = Eliminates Risk" Trap. In cause-effect questions, FPSC takes a measured statement ("reduces risk," "may cause," "is associated with") and offers conclusions that use absolute language ("always," "never," "will definitely"). These absolute conclusions never follow from qualified premises. Match the strength of the conclusion to the strength of the premise.
Trap 5 — The Affirming the Consequent Trap. "All successful people exercise. Ali exercises. Therefore Ali is successful." This is invalid. The fact that successful people exercise does not mean all exercisers are successful. FPSC uses this pattern because it sounds logical at first reading. Identify it, reject it.
The 5-Minute Battle Card
Syllogism patterns — the only four you need:
- All A are B + All B are C → All A are C.
- All A are B + No B are C → No A are C.
- Some A are B + All B are C → Some A are C.
- Some A are B + Some B are C → No certain conclusion.
The three rules that never break:
- "All A are B" does NOT reverse to "All B are A." Only "Some B are A" is allowed.
- "Some A are B" does NOT mean most or all. Some = at least one.
- A restatement of a premise is NEVER a valid conclusion.
Statement-conclusion rules:
- The conclusion must derive NEW information from the premises.
- Real-world knowledge is irrelevant — the premises define the logical universe.
- "Reduces risk" never becomes "eliminates risk" in a valid conclusion.
- Match the strength: qualified premise → qualified conclusion only.
Word analogy method:
- State the relationship in a complete sentence first.
- Apply the exact same sentence structure to find the answer.
- Relationship type matters: tool:purpose, part:whole, cause:effect, item:category.
The "None of These" signal:
- All conclusions are restatements of premises → None of these.
- Both premises use "Some" → None of these.
- Every conclusion requires a reversal of All → None of these.
- Every conclusion is stronger than the premise allows → None of these.
Practice MCQs (FPSC Level)
Part A — Basic Recall (Q1–Q5)
Foundational syllogism, analogy, and statement-conclusion drills.
All mangoes are fruits. All fruits are nutritious. Which follows? (1) All mangoes are nutritious. (2) All nutritious things are mangoes.
Show explanation
Pattern: All + All = All → All mangoes are nutritious. Conclusion 2 reverses 'All A are C' to 'All C are A' — invalid reversal.
Trap: Reversal of universal — Conclusion 2 reads like a tidy mirror but inverts the chain illegally.
Repeated CSS MPT 2022, 2024
No fish are mammals. All dolphins are mammals. Which conclusion logically follows?
Show explanation
Dolphins are entirely within mammals; fish are entirely outside mammals — therefore dolphins and fish share no members.
Trap: Options A, B, D all contradict 'No fish are mammals' in different ways.
Repeated CSS MPT 2023
Pen : Write :: Knife : ?
Show explanation
Relationship is Tool → its specific function. A pen is used to write; a knife is used to cut.
Trap: Sharp (property), Metal (material), Kitchen (location) all share a domain but mismatch the relationship type.
Repeated CSS MPT 2022, 2023
Statement: "Regular reading improves vocabulary." Which conclusion follows?
Show explanation
"Improves" is a qualified positive effect — not a guarantee, not the only path. "May help develop better vocabulary" preserves the qualification.
Trap: Absolute options (A, C, D) over-extend the qualified premise.
Repeated CSS MPT 2024
All doctors are graduates. Some graduates are wealthy. Which follows? (1) Some doctors are wealthy. (2) All wealthy people are doctors.
Show explanation
Pattern: All A are B + Some B are C. The 'Some B' that are C might come entirely from the non-doctor graduates. We cannot conclude any A (doctors) are C (wealthy).
Trap: Conclusion 1 looks intuitive — but the All + Some pattern yields nothing certain about A and C.
FPSC Elite Trap — Some + All pattern
Part B — Trap-Based (Q6–Q10)
Restatement, affirming-the-consequent, and qualified-conclusion traps.
Some candies are lemon-flavoured. Some candies are blue-coloured. Which conclusion follows?
Show explanation
Pattern: Some + Some → no definite conclusion. (A) is a restatement of the premise (not valid). (B), (C) assume overlap not given.
Trap: Option A is the restatement bait — feels 'obviously true' but adds no new information.
Confirmed CSS MPT 2023 Special Q110
All successful business owners work hard. Hamid works hard. Therefore:
Show explanation
Affirming the consequent: All A → B, Hamid is B → Hamid is A? Invalid. Working hard is true of many non-business-owners too.
Trap: Option A is the natural-sounding but invalid leap; FPSC's signature affirming-the-consequent bait.
FPSC Elite Trap — Affirming the consequent
All A are B. All C are B. Which follows?
Show explanation
A and C are both subsets of B. Since ALL A are B, every member of A is also in B. Therefore at least Some B are A.
Trap: A, B, D all assume an A↔C relationship that the premises never establish.
FPSC Elite Trap — Two groups sharing one category
Book : Library :: Painting : ?
Show explanation
Relationship: object → the institution where it is kept and displayed. A book is housed in a library; a painting is housed in a museum.
Trap: Artist (creator), Brush (tool), Canvas (material) are domain-adjacent but break the institution relationship.
Repeated CSS MPT 2023, 2024
Statement: "The government reduced fuel prices by 10%." Which conclusion logically follows?
Show explanation
A 10% fuel cut is one input change — qualified language ('may lead to lower costs') matches the strength of the premise.
Trap: Options A, B, D all use absolute language ('definitely', 'eliminated', 'all') beyond what the premise supports.
FPSC Elite Trap — Qualified vs. absolute conclusion
Part C — Elite Simulation (Q11–Q15)
Highest-difficulty deduction, validity, and correlation traps.
Some birds cannot fly. All penguins are birds. Which follows? (1) Some birds are penguins. (2) Penguins cannot fly.
Show explanation
Conclusion 1 follows: penguins are a subset of birds, so some birds (the penguins) are penguins. Conclusion 2 uses real-world knowledge — the premise only says SOME birds cannot fly, which need not include penguins.
Trap: Real-world knowledge of penguins biases candidates toward accepting Conclusion 2 — but it does not follow from the given premises.
FPSC Elite Trap — Real-world knowledge vs. logical deduction
All roses are flowers. All flowers need water. No stones need water. Which conclusion definitely follows?
Show explanation
All roses → flowers → need water. No stones need water → things that need water cannot be stones → roses cannot be stones.
Trap: Option A is a universal reversal; C and D contradict the premises outright.
FPSC Elite Trap — Three-premise chain
"All champions train daily. Sara trains daily. Therefore Sara is a champion." This argument is:
Show explanation
Affirming the consequent: All A → B, Sara is B → Sara is A. Invalid structure — many daily trainers are not champions.
Trap: "Valid and sound" / "valid but unsound" both wrongly accept the argument as valid; "sound but invalid" is logically impossible.
FPSC Elite Trap — Identifying logical validity
Show explanation
Statement 1 ✓ — valid partial conversion. Statement 2 ✗ — Some + Some yields nothing certain. Statement 3 ✓ — restatement is tautology.
Trap: Statement 2 is the planted error — sounds logical because both premises share B.
FPSC Elite Trap — Statement 2 is the planted error
Statement: "In countries where people eat more fish, the rate of heart disease is lower." Which conclusion most logically follows?
Show explanation
The statement describes a correlation — not a proven cause. 'Associated with lower rates' matches the qualified language precisely.
Trap: A confuses correlation with causation; C and D over-extend the data with absolute claims.
FPSC Elite Trap — Association vs. causation
Answer Key & Full Solutions
Chapter 29 — Syllogisms, Analogies & Logical Deduction
| Q | Correct | Type | Primary Trap | Why Others Fail |
|---|
60-Second Revision
| Category | Key Point |
|---|---|
| Supreme Rule | The given statements are 100% true for the purpose of the question. Real-world knowledge is irrelevant. |
| All + All | All A are B + All B are C → All A are C (certain) |
| Some + All | Some A are B + All B are C → Some A are C (certain) |
| All + No | All A are B + No B are C → No A are C (certain) |
| Some + Some | No certain conclusion is possible — answer is always None of these |
| All + Some (TRAP) | All A are B + Some B are C → NO conclusion about A and C |
| Reversal rule | "All A are B" only reverses to "Some B are A" — NEVER "All B are A" |
| Restatement rule | A restatement of a premise is NOT a valid conclusion |
| Conclusion strength | Match conclusion strength to premise strength: qualified → qualified only |
| Affirming consequent | "All A are B. X is B. Therefore X is A" — INVALID. B applies to many non-A people. |
| Valid vs. sound | Valid = conclusion follows from premises. Sound = valid + premises true. FPSC tests validity only. |
| Statement & conclusion | The conclusion must derive NEW information — not restate or use outside knowledge. |
| Cause & effect | "Reduces risk" never becomes "eliminates risk." Eliminate absolute conclusions from qualified premises. |
| Word analogy method | State relationship as a complete sentence. Apply exact same structure. Check direction. |
| "None of these" signal | All conclusions are restatements, reversals, or stronger than the premise → None of these |