36  Inferences

36.1 Introduction

An inference is a conclusion logically drawn from given statements, data, or observations.
In reasoning exams, inference questions test your ability to analyze provided information and identify what can be reasonably concluded—not assumed, guessed, or imagined.

36.2 1) What is an Inference?

  • Definition: An inference is “a conclusion that logically follows from the facts given.”
  • Unlike assumptions (unstated beliefs), inferences are deductions from data.
  • Unlike probably true/false, inferences are stronger logical consequences.

36.3 2) Approach to Solve

  1. Read the statement(s) carefully.
  2. Do not add external knowledge—treat the statement as absolute truth.
  3. Check each possible inference:
    • If it necessarily follows → inference is valid.
    • If it does not follow → invalid.
    • If information is insufficient → cannot be inferred.

36.4 3) Types of Inferences

  • Certain Inference: Must follow directly from facts.
  • Probable Inference: Reasonable but not guaranteed.
  • Negative Inference: Concludes what cannot be true based on the facts.
  • Cause–Effect Inference: Deduces relationship between two events.

36.5 4) Examples

36.5.1 Example 1

Statement: “All MBA students study Statistics.”
Inferences:
1. Some MBA students do not study Statistics. → Invalid
2. Statistics is a subject for MBA students. → Valid
3. Anyone who does not study Statistics cannot be an MBA student. → Valid

36.5.2 Example 2

Statement: “Many companies are investing in Artificial Intelligence.”
Inferences:
1. All companies are investing in AI. → Invalid
2. AI is becoming popular among companies. → Valid
3. Companies that do not invest in AI will fail. → Cannot be inferred

36.5.3 Example 3

Statement: “The price of petrol increased sharply in the last week.”
Inferences:
1. Petrol is costlier this week than the previous week. → Valid
2. Diesel prices also increased. → Cannot be inferred
3. Sharp price changes can affect transportation cost. → Probable inference

36.6 5) Practice Questions

36.6.1 Q1

Statement: “All schools in the district have libraries.”
Possible inferences:
(a) Students can borrow books from school.
(b) At least one school does not have a library.
(c) Library facilities are available in every school of the district.
(d) Some schools have laboratories.

36.6.2 Q2

Statement: “Some doctors are politicians.”
Possible inferences:
(a) Some politicians are doctors.
(b) All doctors are politicians.
(c) At least one doctor is a politician.
(d) No doctor is a politician.

36.6.3 Q3

Statement: “Due to heavy rains, several trains were delayed.”
Possible inferences:
(a) Some trains ran late because of heavy rains.
(b) All trains were cancelled.
(c) Passengers faced inconvenience.
(d) Weather conditions were bad.

36.7 6) Suggested Answers

  • Q1: (a) Cannot be inferred, (b) Invalid, (c) Valid, (d) Cannot be inferred
  • Q2: (a) Valid (conversion of “some”), (b) Invalid, (c) Valid, (d) Invalid
  • Q3: (a) Valid, (b) Invalid, (c) Probable inference, (d) Valid

36.8 Summary

  • Inference = logical conclusion drawn from given statements only.
  • Do not mix with assumptions or guesses.
  • Keywords: “all,” “some,” “many,” “most” → be precise.
  • Always check whether the inference must follow or is only probable.