Statement & conclusion: Reasoning Ability Notes for Nagaland Patwari / Lekhpal

Statement & Conclusion – Reasoning Ability

(For the Nagaland Patwari / Lekhpal Examination)

Term	Meaning
Statement	A fact or a set of facts given in the problem. It can be one or several sentences.
Conclusion	A claim that follows (or does not follow) logically from the statements. The test asks you to decide whether each conclusion is always true, sometimes true, or never true given the statements.

Typical format:

Statements  
1. All A are B.  
2. Some C are not A.  

Conclusions  
I. Some B are C.  
II. No C are B.

You must pick the correct answer:

Read every statement carefully – note the quantifiers (All, No, Some, Some not, etc.).
Translate into Venn–diagram language (if you’re comfortable) or use logical symbols.
Check each conclusion against the statements:
- If the conclusion is logically implied by the statements → it is true.
- If the statements allow a counter‑example to the conclusion → it is false.
- If the conclusion can be either true or false (both possibilities exist) → it is undetermined (neither always true nor always false).

The key is universal (always true) vs possible (sometimes true) vs impossible (always false).

Step	What to do	Why it matters
A. Identify quantifiers	All, No, Some, Some not	Determines the scope of the claim.
B. Visualise or symbolise	Use Venn diagrams, set notation, or propositional logic	Helps see overlaps and exclusions.
C. Look for contradictions	If a conclusion contradicts a statement → impossible.	Eliminates false conclusions.
D. Look for “necessary” inference	If every element satisfying the statement must satisfy the conclusion	Valid conclusion.
E. Look for “sufficient” inference	If the conclusion is true in at least one scenario consistent with statements	Not necessarily valid.
F. Check for hidden assumptions	Example: “All A are B” does not mean “All B are A”.	Avoids over‑generalisation.
G. Keep track of “some” vs “all”	“Some A are B” does not guarantee “All A are B”.	Prevents false universal conclusions.

Statements

All S are T.

Some U are S.

No V are U.

Some V are T.

Conclusions
I. Some S are V.
II. Some T are U.
III. No U are T.
IV. Some T are V.

Conclusion	Analysis	Verdict
I. Some S are V	We know No V are U and Some U are S. That does not forbid S from overlapping V. The only restriction is that V cannot intersect U. Since S may or may not intersect V, this conclusion is undetermined.
II. Some T are U	From (1) All S are T. From (2) Some U are S → Those U are also T (by transitivity). Hence there must be at least one element that is both T and U. So true.
III. No U are T	Contradicts conclusion II (which says some U are T). Thus false.
IV. Some T are V	Statement (4) gives “Some V are T”. Since “Some V are T” is symmetric, this is true.

So the correct answer would be B (Only II and IV are correct).

Transitivity of “All A are B” and “Some B are C” → “Some A are C”.
“No A are B” + “Some B are C” only tells you that the intersection of A and C is possible but not guaranteed.
Symmetry of “Some A are B” (if some A are B, some B are A).

Item	Take‑away
Understand quantifiers	`All`, `No`, `Some`, `Some not` – each changes the inference.
Use Venn diagrams	A quick visual check for overlaps and exclusions.
Check for contradictions	A conclusion that directly contradicts a statement is immediately false.
Look for necessary inference	If every element satisfying the antecedent must satisfy the consequent → conclusion is true.
Beware of over‑generalisation	“All A are B” ≠ “All B are A”.
Keep “some” vs “all” in mind	“Some A are B” does NOT imply “All A are B”.
Transitivity rule	`