Each of the following two items 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. Codes:

This question is a classic application of **Syllogism** and the **Square of Opposition**, a fundamental concept in Deductive Logic often tested in the UPSC CSAT. To solve this, we must first understand the logical relationship defined in the prompt. --- ### Step 1: Understand the Logical Condition The question asks for two statements that: 1. **Cannot both be true** (at least one must be false). 2. **Can both be false** (it is possible that neither statement is true). In formal logic, this specific relationship is known as a **Contrary Relationship**. ### Step 2: Categorize the Statements In logic, there are four types of categorical propositions: * **A (Universal Affirmative):** "All S are P" (e.g., *All animals are carnivorous*) * **E (Universal Negative):** "No S are P" (e.g., *Animals are not carnivorous*) * **I (Particular Affirmative):** "Some S are P" (e.g., *Some animals are carnivorous*) * **O (Particular Negative):** "Some S are not P" (e.g., *Some animals are not carnivorous*) Let’s map the given statements: 1. **Statement 1:** "All animals are carnivorous" — **Type A** 2. **Statement 2:** "Some animals are not carnivorous" — **Type O** 3. **Statement 3:** "Animals are not carnivorous" (means *No animals are carnivorous*) — **Type E** 4. **Statement 4:** "Some animals are carnivorous" — **Type I** ### Step 3: Analyze the Relationships (The Square of Opposition) To find the pair that satisfies the "Contrary" condition, we look at how these types interact: * **Contradictories (A & O, E & I):** One must be true and the other must be false. They cannot both be true, and they **cannot** both be false. * **Contraries (A & E):** They **cannot both be true**, but they **can both be false**. This occurs when the truth lies somewhere in the "Some" category. * **Sub-contraries (I & O):** They can both be true, but they cannot both be false. ### Step 4: Evaluate the Options #### Option A: 1 and 3 (Type A and Type E) * **Statement 1:** All animals are carnivorous. * **Statement 3:** No animals are carnivorous. * **Reasoning:** If it is true that *all* animals are carnivorous, it is impossible for it to be true that *none* are. Thus, they **cannot both be true**. * **Can they both be false?** Yes. If, in reality, *some* animals are carnivorous and *some* are not (which is the case in the real world), then both "All" and "None" are false statements. * **Conclusion:** This matches the condition perfectly. #### Option B: 1 and 2 (Type A and Type O) * These are **Contradictories**. If Statement 1 is false, Statement 2 *must* be true. They cannot both be false. #### Option C: 2 and 3 (Type O and Type E) * These are related by **Sub-alternation**. If Statement 3 ("None") is true, then Statement 2 ("Some not") must also be true. They can both be true. #### Option D: 3 and 4 (Type E and Type I) * These are **Contradictories**. Like Option B, one must be true and the other false. They cannot both be false. --- ### Final Summary for the Aspirant * **The Condition:** "Cannot both be true, but can both be false" = **Contrary Relationship**. * **The Rule:** Contraries always exist between the two **Universal** statements (**All** vs. **None**). * **The Answer:** Statement 1 ("All") and Statement 3 ("None/Not") are the universals. Therefore, the correct answer is **A**.