Reasoning : Logical Reasoning & Analytical Ability

Q 324 / 325

UPSC CSE Prelims 2011

The question below consists of four statements. Of these four statements, two cannot both be true, but both can be false. Study the statements carefully and identify the two that satisfy the above condition. Select the correct answer using the codes given below each set of statements:
Examine the following statements:
  1. All animals are carnivorous.
  2. Some animals are not carnivorous.
  3. Animals are not carnivorous.
  4. Some animals are carnivorous.

EXPLANATION

Correct Option (A)

Statements 1 ("All animals are carnivorous") and 3 ("Animals are not carnivorous," which is logically equivalent to "No animals are carnivorous") are classified as contrary propositions within the traditional Square of Opposition.

  • Contrary propositions cannot both be true simultaneously. If Statement 1 is true, Statement 3 must be false, and conversely.
  • However, contrary propositions can both be false. For instance, if some animals are carnivorous (Statement 4) and some animals are not carnivorous (Statement 2), then both Statement 1 and Statement 3 would be false.

This characteristic precisely matches the condition that the two statements "cannot both be true, but both can be false."

Incorrect Options:

The other pairs do not satisfy the specified logical condition:

  • 1 & 2: Statement 1 ("All animals are carnivorous") and Statement 2 ("Some animals are not carnivorous") are contradictory propositions. Contradictories cannot both be true, nor can they both be false. If one is true, the other must be false, and vice-versa.
  • 2 & 3: Statement 2 ("Some animals are not carnivorous") and Statement 3 ("No animals are carnivorous") can both be true. If "No animals are carnivorous" (Statement 3) is true, it logically implies that "Some animals are not carnivorous" (Statement 2) is also true. This violates the condition that the statements "cannot both be true."
  • 3 & 4: Statement 3 ("No animals are carnivorous") and Statement 4 ("Some animals are carnivorous") are contradictory propositions. Similar to 1 & 2, contradictories cannot both be true, and they cannot both be false.