Given below are four statements.

Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not

Question

Given below are four statements.

Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.

From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

Statement 1 and Statement 3

Statement 1 and Statement 2

Statement 2 and Statement 4

Statement 3 and Statement 4
No, the answer is incorrect.
Score: 0
Accepted Answers:
Statement 1 and Statement 3
Gate Mock Test, Gate Practice Test question, Answer carefully with all clear steps and accuracy with given answer:9) Given below are four statements. point
Statment 1: Al students ar nus.
Statement 2 Some student are inquisitive.
Sstment No student fs qui.
‘Statament 4: Some students ae not nqsive.
From the gen fou statements ind he two statements that CANNOT BE TRUE siultanecusly, assuring that theres a ast ane student i the cass.
Statement 1 and Statement 3
‘Statement 1 and Statement 2
Statement 2 and Statement 4
‘Statement 3 and Sistemen 4
No, the answer i Incorrect.
score:
‘Accepted Answers:
Sest

VIPSolutions · Accepted Answer

Let's analyze the statements carefully:

### Statements:
1. **All students are inquisitive**  
2. **Some students are inquisitive**  
3. **No student is inquisitive**  
4. **Some students are not inquisitive**

---

### Logical implications:

- **Statement 1:** All students are inquisitive.  
  - This implies every student is inquisitive, so there are no students who are not inquisitive.

- **Statement 2:** Some students are inquisitive.  
  - This indicates at least one student is inquisitive, but doesn't specify all students.

- **Statement 3:** No student is inquisitive.  
  - This is mutually exclusive with Statement 1 because if all students are inquisitive, then not a single student can be non-inquisitive.

- **Statement 4:** Some students are not inquisitive.  
  - This is incompatible with Statement 1, which states all students are inquisitive.

---

### Which statements cannot be true simultaneously?

- **Statement 1** and **Statement 3**:  
  - These are directly contradictory. Statement 1 says all students are inquisitive, while Statement 3 says no student is inquisitive.  
  - They **cannot** both be true **at the same time**.

- **Statement 1** and **Statement 2**:  
  - These can both be true because if all students are inquisitive, then it is true that some students are inquisitive.

- **Statement 2** and **Statement 4**:  
  - These can both be true because "some students are inquisitive" and "some students are not inquisitive" can both happen if the class has a mixed group.

- **Statement 3** and **Statement 4**:  
  - These can both be true because if no student is inquisitive, then necessarily some students are not inquisitive.

---

### Conclusion:
The **only pair** that **cannot** be true simultaneously is **Statement 1** and **Statement 3**.

**Answer:**  
**Statement 1 and Statement 3**

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