Statement & conclusion: Reasoning Ability Notes for Arunachal Pradesh Police Constable

Study Notes – Reasoning Ability

Topic: Statement & Conclusion
Exam: Arunachal Pradesh Police Constable (ALPC)
Format: 10 questions, 5 minutes, 1 mark each

1. Simple Explanation

What	Why	How
Statement	The facts or observations given in the problem.	List them clearly – they are the only reliable data.
Conclusion	A claim that may or may not follow from the statements.	Test if the conclusion is necessarily true, impossible, or cannot be determined.
Reasoning	Uses logical deduction (inference, transitivity, negation, etc.).	Apply the rules of inference systematically.

Goal:

From the set of statements, decide which conclusion(s) are logically valid (must be true), invalid (cannot be true), or indeterminate (insufficient information).

2. Key Points

#	Key Point	Tips
1	Statements are absolute.	Treat them as facts; no hidden assumptions.
2	Do not add extra facts.	Only use what is explicitly stated.
3	Logical operators: • AND (conjunction) – both conditions true. • OR (disjunction) – at least one true. • NOT (negation) – opposite. • IF…THEN (implication).	Recognise them in wording: “if … then”, “unless”, “provided that”.
4	Transitive inference.	From A → B and B → C, deduce A → C.
5	Contrapositive.	From A → B, deduce ¬B → ¬A.
6	Reductio ad absurdum.	Assume the opposite of the conclusion and show a contradiction with the statements.
7	Multiple conclusions.	Only one of the listed conclusions will be correct; others are “cannot be determined” or “false”.
8	Time‑saving trick: Write the statements in a bullet list or table before starting.	Keeps the logic clear and reduces re‑reading.
9	Beware of “only” / “exactly” / “always”.	These words force exclusivity; handle them carefully.
10	Check for “cannot be determined”.	If the statements do not force a truth value, the conclusion is indeterminate.

3. Worked Example

3.1 Problem Statement

Statements

If a person is a policeman, then he is a male.

If a person is a female, then she is not a policeman.

If a person is a teacher, then she is a female.

If a person is a policeman, then he is a teacher.

Conclusion
(C) The person is a policeman.

Which of the following is true?
A. The conclusion is necessarily true.
B. The conclusion is necessarily false.
C. The conclusion cannot be determined.

3.2 Step‑by‑Step Reasoning

Step	Logic	Explanation
1	List the statements in bullet form.	1. P → M 2. F → ¬P 3. T → F 4. P → T
2	Identify relationships.	From 4: P → T. From 3: T → F. Therefore P → F (transitive).
3	Combine with 1.	P → M (given). Also P → F (deduced).
4	Check for contradiction.	1 says if P then M. 2 says if F then ¬P. But we have P → F, so P would imply F. If P implies F, then F implies ¬P, so P implies ¬P → contradiction.
5	Conclude impossibility.	The assumption that a person is a policeman leads to a logical contradiction. Therefore no one can be a policeman under these statements.
6	Evaluate conclusion.	Since “The person is a policeman” is impossible, the conclusion is necessarily false.

3.3 Answer

B. The conclusion is necessarily false.

4. Quick Revision Summary

Section	What to Review	Quick Tip
Statements	Treat them as facts only.	Write them out before attempting conclusions.
Logical Operators	AND, OR, NOT, IF…THEN.	Look for key words: “if”, “unless”, “only”.
Inference Rules	Transitivity, contrapositive, contradiction.	Practice: P → Q & Q → R → P → R.
Conclusion Types	True, False, Indeterminate.	Remember: True = must follow; False = impossible; Indeterminate = not forced.
Common Pitfalls	Adding unstated facts, misreading “only”, ignoring negations.	Double‑check each inference step.
Time Management	5 minutes for 10 questions = 30 s each.	Use the “write statements first” trick to avoid re‑