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

Statement & Conclusion – Reasoning Ability

Program: Punjab Patwari / Lekhpal
Exam Series: Reasoning Ability – Question Type “Statement & Conclusion”

This type of question tests your ability to infer logical conclusions from a set of statements.
You must decide whether a conclusion follows necessarily, possibly, or does not follow from the statements.

1. Simple Explanation

Term	Meaning	Example
Statement	A factual claim that is given as true in the problem.	“All roses are flowers.”
Conclusion	A claim that you are asked to judge based on the statements.	“Some flowers are roses.”
Inference	The logical step that connects the statement(s) to the conclusion.	From “All roses are flowers” ⇒ “Some flowers are roses” (conclusion is possible).

Goal:
For each question, choose the option that correctly describes the relationship between the statements and the conclusion.

2. Key Points (Quick Reference)

#	Point	Why It Matters
1	Types of Inferences	• Necessary: must be true if statements are true. • Possible: could be true but not guaranteed. • Impossible: cannot be true given statements.
2	Logical Connectors	• All/Any/Every → universal quantifier. • Some/Any/Some → existential quantifier. • None/No → negation.
3	Rule of Inference	• Universal → Existential (All A are B ⇒ Some B are A → possible). • Existential → Universal (Some A are B → Not necessarily All B are A).
4	Contrapositive	If “All A are B” → “No B is non‑A.” Use to deduce negative conclusions.
5	Transitivity	If A → B and B → C, then A → C.
6	Avoid Over‑Generalisation	Do not infer “All” from “Some.”
7	Check for Contradiction	If a conclusion contradicts a given statement, it is impossible.
8	Write Down the Statements	Helps visualise relationships (Venn diagram or simple tables).

3. Worked Example

Statements

| S1 | All students are learners. | | S2 | Some learners are athletes. |

Conclusion (C)
Some students are athletes.

Step‑by‑Step Reasoning

Translate to Logical Form
- S1: ∀x (Student(x) → Learner(x))
- S2: ∃x (Learner(x) ∧ Athlete(x))
- C: ∃x (Student(x) ∧ Athlete(x))
Analyse Relationships
- From S1 we know every student belongs to the set “learners.”
- From S2 we know there exists at least one learner who is also an athlete.
Determine Possibility
- The athlete in S2 could be a student (since all students are learners).
- But the athlete could also be a non‑student learner.
Conclusion
- Because we cannot be sure that the athlete in S2 is a student, the conclusion is possibly true but not necessary.
Pick the Correct Option
- (B) Possible (if the options are: 1) Necessary, 2) Possible, 3) Impossible, 4) Both necessary & possible).

Visual Aid (Venn)

  +--------------+      +--------------+
  |   Students   |      |   Athletes   |
  |  (Students)  |      | (Athletes)   |
  +--------------+      +--------------+
         \                /
          \              /
           \   Learners /
            \          /
             \        /
              \______/

All students lie in the “Learners” circle.
Some learners lie in the “Athletes” circle.
Intersection of “Students” and “Athletes” might be empty or not – unknown.

4. Quick Revision Summary

Item	What to Remember	Quick Check
Statement & Conclusion	Statements are givens; conclusions are to be judged.	Read all statements first.
Inference Types	Necessary, Possible, Impossible.	Can you prove it must be true?
Universal → Existential	All A are B → Some B are A → possible.	Look for “All” → “Some”.
Existential → Universal	Some A are B → All B are A → impossible.	Avoid “All” from “Some”.
Contrapositive	All A are B → No B is not‑A.	Use negation when needed.
Transitivity	A→B & B→C → A→C.	Chain the statements.
Common Mistakes	• Assuming “All” from “Some”. • Ignoring the possibility of overlapping sets. • Confusing “No” with “Some”.	Double‑check each logical step.
Typical Questions	1. Two statements (S1, S2) and one conclusion (C). 2. Options: Necessary, Possible, Impossible, Both.	Identify the minimal inference needed.

One‑Minute Recap

Read all statements – note quantifiers (“All”, “Some”, “None”).
Translate into logical form or draw a Venn diagram.
Determine if the conclusion must follow, could follow, or cannot follow.
Select the appropriate option.