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Logical Consistency

Logical consistency means that the statements, conclusions, or answers in a problem do not contradict one another. In SSC, Railway, Bank, and State exams, this skill is tested through statement–conclusion questions, syllogisms, cause-and-effect questions, and "which option is logically consistent" questions. This chapter builds the core ideas step by step.

1. What is Logical Consistency?

A set of statements is logically consistent if all of them can be true at the same time. If two statements cannot both be true, they are inconsistent (contradictory).

• Consistent: "All pens are blue." + "This is a pen." → This pen must be blue. No clash.
• Inconsistent: "All pens are blue." + "This pen is red." → Both cannot be true together.

Exam tip: In these questions, treat the given statements as 100% true, even if they sound false in real life (e.g., "All cats are dogs"). Your job is to check what *follows logically*, not what is true in the world.

2. Key Building Blocks

2.1 Statement and Conclusion

• A statement is given information.
• A conclusion is something that must be true if the statements are true.
• A conclusion is valid only if it follows in every possible case, not just in one possible arrangement.

2.2 Types of Statements (Syllogism Basics)

2.3 Golden Rules of Syllogism

1. From two particular statements (Some…, Some…), no definite conclusion follows.
2. From two negative statements, no definite conclusion follows.
3. If one statement is particular, the conclusion (if any) must be particular.
4. If one statement is negative, the conclusion (if any) must be negative.
5. "All A are B" does not mean "All B are A". But "Some B are A" does follow from "All A are B".
6. "No A is B" also means "No B is A" (negative statements convert fully).

2.4 Venn Diagram Method

Draw circles for each term and shade/mark according to the statements. Then test each conclusion:

• If the conclusion holds in every valid diagram → it follows.
• If even one valid diagram breaks it → it does not follow.

3. Common Exam Traps

• Real-life bias: Rejecting a conclusion because it sounds odd in real life. Logic, not reality, decides.
• "All" reversed: Assuming "All A are B" gives "All B are A". It does not.
• Possibility vs. certainty: "Some A may be B" (possibility) can be correct even when "Some A are B" (definite) is not. Read the wording carefully.
• Either–or case: When two conclusions are contradictory (one positive, one negative about the same terms) and neither follows alone, but one of them must be true, the answer is "either I or II follows".
• Negative wording: "Which does NOT follow" — underline the NOT before solving.

4. Solved Examples

Example 1
Statements: All dogs are animals. All animals are living beings.
Conclusions: I. All dogs are living beings. II. Some living beings are dogs.

*Solution:* Dogs ⊂ Animals ⊂ Living beings. So all dogs are living beings (I follows), and therefore some living beings are dogs (II follows). Both follow.

Example 2
Statements: Some pens are pencils. Some pencils are erasers.
Conclusions: I. Some pens are erasers. II. No pen is an eraser.

*Solution:* Two particular statements give no definite conclusion. Neither I nor II follows definitely. But I and II are contradictory, and one of them must be true. Answer: Either I or II follows.

Example 3
Statements: No chair is a table. All tables are desks.
Conclusions: I. No chair is a desk. II. Some desks are not chairs.

*Solution:* Chairs may or may not overlap with desks, so I does not follow. Since all tables are desks and no chair is a table, the part of desks that are tables is not chairs — so some desks are not chairs. Only II follows.

5. Quick Strategy for the Exam

1. Read statements; accept them as true.
2. Draw a quick Venn diagram (10–15 seconds).
3. Test each conclusion against the diagram.
4. Check for the either–or case only when neither conclusion follows alone.
5. Skip "real life" thinking entirely.

6. Practice Questions

Q1. Statements: All books are pages. All pages are papers.
Conclusions: I. All books are papers. II. Some papers are books.
(a) Only I follows (b) Only II follows (c) Both follow (d) Neither follows
Answer: (c)
Solution: Books ⊂ Pages ⊂ Papers, so all books are papers, and hence some papers are books. Both conclusions follow.
Source: PYQ-style

Q2. Statements: Some boys are students. Some students are players.
Conclusions: I. Some boys are players. II. No boy is a player.
(a) Only I follows (b) Only II follows (c) Either I or II follows (d) Both follow
Answer: (c)
Solution: Two particular statements give no definite conclusion, but I and II are contradictory, so exactly one must be true — either–or case.
Source: PYQ-style

Q3. Statements: No flower is a leaf. All leaves are green.
Conclusions: I. No flower is green. II. Some green things are not flowers.
(a) Only I follows (b) Only II follows (c) Both follow (d) Neither follows
Answer: (b)
Solution: Flowers may still be green through other categories, so I fails. The green things that are leaves cannot be flowers, so II follows.
Source: PYQ-style

Q4. Statements: All cups are plates. No plate is a spoon.
Conclusions: I. No cup is a spoon. II. Some plates are cups.
(a) Only I follows (b) Only II follows (c) Both follow (d) Neither follows
Answer: (c)
Solution: Cups are inside plates, and plates are fully outside spoons, so no cup is a spoon. "All cups are plates" also gives "some plates are cups".
Source: PYQ-style

Q5. Statements: Some teachers are doctors. All doctors are honest.
Conclusions: I. Some teachers are honest. II. All teachers are honest.
(a) Only I follows (b) Only II follows (c) Both follow (d) Neither follows
Answer: (a)
Solution: The teachers who are doctors are honest, so some teachers are honest. Nothing says all teachers are doctors, so II fails.
Source: PYQ-style