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True / False / Uncertain Type Deduction

Introduction

In reasoning-based questions, you are often asked to decide whether a given statement is True, False, or Cannot Be Determined (Uncertain) from the provided information. This pattern tests your ability to interpret facts exactly as given-no assumptions, no imagination.

It is one of the most fundamental analytical reasoning patterns, helping you build logical precision for Data Sufficiency, Critical Reasoning, and Logical Deduction sets.

Pattern: True / False / Uncertain Type Deduction

Pattern

The key idea is to evaluate statements against given facts - deciding whether each statement is definitely true, definitely false, or cannot be determined from the given data.

- True → Must follow logically from the given information.
- False → Directly contradicts the given information.
- Uncertain → Neither directly follows nor contradicts - insufficient data.

Step-by-Step Example

Question

Passage:
“All managers in the company have at least five years of experience. Some team leads have less than five years of experience. Ritu is a manager in the same company.”

Statements:
(1) Ritu has at least five years of experience.
(2) Ritu is also a team lead.

Which of the above statements are True, False, or Uncertain?
(A) Both True
(B) Both False
(C) Statement (1) True, (2) Uncertain
(D) Statement (1) True, (2) False

Solution

  1. Step 1: Analyze Statement (1)

    All managers → have ≥5 years experience. Ritu is a manager ⇒ she definitely has ≥5 years. ✅ True.

  2. Step 2: Analyze Statement (2)

    No information connects Ritu with team leads. It’s possible but not given ⇒ ❓ Uncertain.

  3. Final Answer:

    Statement (1) True, Statement (2) Uncertain → Option C

  4. Quick Check:

    Direct deduction for (1), lack of link for (2) ⇒ True + Uncertain ✅

Quick Variations

1. Classify individual statements as True/False/Uncertain.

2. Identify which among multiple statements are definitely true.

3. “Cannot be determined” style questions in data-based reasoning.

4. Table- or paragraph-based factual evaluation tasks.

Trick to Always Use

  • Step 1: Read the passage carefully - treat it as 100% true.
  • Step 2: Compare each statement directly to the facts.
  • Step 3: If not explicitly supported or denied, mark “Uncertain.”
  • Step 4: Never assume anything beyond what is stated.

Summary

Summary

  • “True” means it must follow logically from given facts.
  • “False” means it contradicts the given facts directly.
  • “Uncertain” means the data is insufficient to conclude either way.
  • Carefully differentiate between lack of information and contradiction.

Example to remember:
“All cats are animals. Some animals are dogs.” → ‘All cats are dogs’ = False; ‘Some animals are cats’ = True; ‘Some cats are dogs’ = Uncertain.

Practice

(1/5)
1. Passage:<br>“All players in the cricket team are fit. Some players are bowlers. Raj is a bowler in the team.”<br><br>Statements:<br>(1) Raj is fit.<br>(2) All bowlers are unfit.<br><br>Which of the above statements are True, False, or Uncertain?<br>(A) (1) True, (2) False<br>(B) (1) True, (2) Uncertain<br>(C) (1) Uncertain, (2) False<br>(D) Both True
easy
A. (1) True, (2) False
B. (1) True, (2) Uncertain
C. (1) Uncertain, (2) False
D. Both True

Solution

  1. Step 1: Analyze (1)

    All players in the team are fit. Raj is a player, so he is fit → ✅ True.

  2. Step 2: Analyze (2)

    Statement says all bowlers are unfit - contradicts the given passage where all players (including bowlers) are fit → ❌ False.

  3. Final Answer:

    (1) True, (2) False → Option A

  4. Quick Check:

    Raj is part of “all players are fit” ⇒ fits logic ✅
Hint: When a universal statement applies to all, it covers every subset automatically.
Common Mistakes: Marking the second statement as Uncertain instead of False.
2. Passage:<br>“Some fruits are sweet. All mangoes are fruits. Some fruits are sour.”<br><br>Statements:<br>(1) All mangoes are sweet.<br>(2) Some mangoes may be sweet.<br><br>Which of the above statements are True, False, or Uncertain?<br>(A) (1) False, (2) True<br>(B) (1) False, (2) Uncertain<br>(C) (1) Uncertain, (2) True<br>(D) (1) True, (2) False
easy
A. (1) False, (2) True
B. (1) False, (2) Uncertain
C. (1) Uncertain, (2) True
D. (1) True, (2) False

Solution

  1. Step 1: Analyze (1)

    ‘All mangoes are sweet’ - not stated in passage → ❌ Uncertain.

  2. Step 2: Analyze (2)

    ‘Some mangoes may be sweet’ - possible since some fruits (to which mangoes belong) are sweet → ✅ True.

  3. Final Answer:

    (1) Uncertain, (2) True → Option C

  4. Quick Check:

    Partial truth applies logically to a subset ✅
Hint: ‘Some’ allows possibility, not certainty - check direct inclusion.
Common Mistakes: Assuming all mangoes are sweet without given proof.
3. Passage:<br>“All cars are vehicles. Some vehicles are red. No bike is a car.”<br><br>Statements:<br>(1) Some vehicles are not bikes.<br>(2) All red vehicles are cars.<br><br>Which of the above statements are True, False, or Uncertain?<br>(A) (1) True, (2) Uncertain<br>(B) (1) False, (2) True<br>(C) (1) True, (2) False<br>(D) (1) Uncertain, (2) False
medium
A. (1) True, (2) Uncertain
B. (1) False, (2) True
C. (1) True, (2) False
D. (1) Uncertain, (2) False

Solution

  1. Step 1: Analyze (1)

    No bike is a car and all cars are vehicles → Some vehicles (cars) are not bikes → ✅ True.

  2. Step 2: Analyze (2)

    ‘All red vehicles are cars’ - not given, as red vehicles could include other types → ❌ False.

  3. Final Answer:

    (1) True, (2) False → Option C

  4. Quick Check:

    Logical consistency confirmed ✅
Hint: When exclusion exists, look for direct negation-based deductions.
Common Mistakes: Assuming all red vehicles must be cars.
4. Passage:<br>“Every student who studies regularly passes the exam. Some students do not study regularly.”<br><br>Statements:<br>(1) Some students may fail the exam.<br>(2) All students will pass the exam.<br><br>Which of the above statements are True, False, or Uncertain?<br>(A) (1) True, (2) False<br>(B) (1) Uncertain, (2) True<br>(C) (1) False, (2) True<br>(D) (1) True, (2) Uncertain
medium
A. (1) True, (2) False
B. (1) Uncertain, (2) True
C. (1) False, (2) True
D. (1) True, (2) Uncertain

Solution

  1. Step 1: Analyze (1)

    Some students do not study regularly; only regular students pass ⇒ those who do not may fail → ✅ True.

  2. Step 2: Analyze (2)

    ‘All students will pass’ contradicts passage → ❌ False.

  3. Final Answer:

    (1) True, (2) False → Option A

  4. Quick Check:

    Condition-based deduction validated ✅
Hint: Look for ‘only if’ triggers; absence breaks certainty.
Common Mistakes: Assuming all students succeed despite exceptions.
5. Passage:<br>“All doctors are educated. Some educated people are researchers. No researcher is a farmer.”<br><br>Statements:<br>(1) All doctors are researchers.<br>(2) Some educated people are not farmers.<br><br>Which of the above statements are True, False, or Uncertain?<br>(A) (1) False, (2) True<br>(B) (1) True, (2) False<br>(C) (1) Uncertain, (2) False<br>(D) (1) True, (2) Uncertain
medium
A. (1) False, (2) True
B. (1) True, (2) False
C. (1) Uncertain, (2) False
D. (1) True, (2) Uncertain

Solution

  1. Step 1: Analyze (1)

    ‘All doctors are researchers’ - not mentioned and conflicts with data → ❌ False.

  2. Step 2: Analyze (2)

    Some educated people are researchers, and no researcher is a farmer → hence those researchers (educated) are not farmers → ✅ True.

  3. Final Answer:

    (1) False, (2) True → Option A

  4. Quick Check:

    Subset mapping holds logically ✅
Hint: Map set relations with Venn reasoning to avoid assumption-based errors.
Common Mistakes: Inferring indirect relation between doctors and researchers.

Mock Test

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