Examine the following statements: 1. I watch TV only if I am bored. 2. I am never bored when I have my brother’s company. 3. Whenever I go to the theatre I take my brother along. Which one of the following conclusions is valid in the context of the above statements?

IAS 2012 — CSAT Reasoning

2012mcqmedium

Examine the following statements:

I watch TV only if I am bored.
I am never bored when I have my brother’s company.
Whenever I go to the theatre I take my brother along.

Which one of the following conclusions is valid in the context of the above statements?

Official previous-year question

Verified 2 Aug 2026.

Options

AIf I am bored, I watch TV.
BIf I am bored, I seek my brother’s company.
CIf I am not with my brother, then I watch TV.
DI am not bored, I do not watch TV.

Did you get this right?

Solution

To determine the valid conclusion, let's analyze each statement using conditional logic:

Statement 1: "I watch TV only if I am bored."
- This means: If I watch TV (P), then I am bored (Q). (P → Q)
- The contrapositive is: If I am not bored (¬Q), then I do not watch TV (¬P). (¬Q → ¬P)
Statement 2: "I am never bored when I have my brother’s company."
- This means: If I have my brother’s company (R), then I am not bored (¬Q). (R → ¬Q)
- The contrapositive is: If I am bored (Q), then I do not have my brother’s company (¬R). (Q → ¬R)
Statement 3: "Whenever I go to the theatre I take my brother along."
- This means: If I go to the theatre (S), then I have my brother’s company (R). (S → R)

Correct Option

If I am not bored, I do not watch TV.

This conclusion is the contrapositive of Statement 1. A contrapositive statement is logically equivalent to the original conditional statement. Since Statement 1 (P → Q) is given as true, its contrapositive (¬Q → ¬P) must also be true. Therefore, "If I am not bored, then I do not watch TV" is a valid deduction.

Incorrect Options

Option (A): If I am bored, I watch TV.
This is the converse of Statement 1 (Q → P). Statement 1 (P → Q) establishes that watching TV implies boredom, but it does not assert that boredom necessarily leads to watching TV. The converse of a true statement is not always true.
Option (B): If I am bored, I seek my brother’s company.
From Statement 2 (R → ¬Q), its contrapositive is (Q → ¬R), meaning "If I am bored, then I do not have my brother's company." Option (B) suggests the opposite (Q → R), which directly contradicts the logical inference from Statement 2. Therefore, this conclusion is invalid.
Option (C): If I am not with my brother, then I watch TV.
From Statement 2 (R → ¬Q), its contrapositive is (¬R → Q), meaning "If I am not with my brother, then I am bored." However, as established for Option (A), being bored (Q) does not necessarily imply watching TV (P) according to Statement 1 (P → Q). Therefore, this conclusion cannot be validly drawn.

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To determine the valid conclusion, let's analyze each statement using conditional logic:

Statement 1: "I watch TV only if I am bored."
- This means: If I watch TV (P), then I am bored (Q). (P → Q)
- The contrapositive is: If I am not bored (¬Q), then I do not watch TV (¬P). (¬Q → ¬P)
Statement 2: "I am never bored when I have my brother’s company."
- This means: If I have my brother’s company (R), then I am not bored (¬Q). (R → ¬Q)
- The contrapositive is: If I am bored (Q), then I do not have my brother’s company (¬R). (Q → ¬R)
Statement 3: "Whenever I go to the theatre I take my brother along."
- This means: If I go to the theatre (S), then I have my brother’s company (R). (S → R)

Correct Option

If I am not bored, I do not watch TV.

Incorrect Options

Option (A): If I am bored, I watch TV.
This is the converse of Statement 1 (Q → P). Statement 1 (P → Q) establishes that watching TV implies boredom, but it does not assert that boredom necessarily leads to watching TV. The converse of a true statement is not always true.
Option (B): If I am bored, I seek my brother’s company.
From Statement 2 (R → ¬Q), its contrapositive is (Q → ¬R), meaning "If I am bored, then I do not have my brother's company." Option (B) suggests the opposite (Q → R), which directly contradicts the logical inference from Statement 2. Therefore, this conclusion is invalid.
Option (C): If I am not with my brother, then I watch TV.
From Statement 2 (R → ¬Q), its contrapositive is (¬R → Q), meaning "If I am not with my brother, then I am bored." However, as established for Option (A), being bored (Q) does not necessarily imply watching TV (P) according to Statement 1 (P → Q). Therefore, this conclusion cannot be validly drawn.

IAS 2012 — CSAT Reasoning

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IAS 2012 — CSAT Reasoning

Options

Did you get this right?

Solution

Correct Option

Incorrect Options

Your note

IAS Reasoning in other years

More IAS Reasoning questions

Other CSAT topics for IAS

Comprehension

Maths

Keep practicing Reasoning