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.

• A. Statement 1 and Statement 3
• B. Statement 1 and Statement 2
• C. Statement 2 and Statement 4
• D. Statement 3 and Statement 4

Hint:

When analyzing logical statements, check for contradictions between universal and existential statements. Two mutually exclusive statements cannot both be true at the same time.

Answer 1

The Correct Option is A

To solve the problem of identifying which two statements cannot be true simultaneously, we need to analyze each statement logically.

1. Statement 1: "All students are inquisitive." - This statement means every student in the class is inquisitive. There are no exceptions.
2. Statement 2: "Some students are inquisitive." - This statement implies there is at least one student who is inquisitive, but not necessarily all students are inquisitive.
3. Statement 3: "No student is inquisitive." - This statement suggests that not a single student in the class is inquisitive.
4. Statement 4: "Some students are not inquisitive." - This indicates that there exists at least one student who is not inquisitive.

Now, let's evaluate the combinations:

• Statement 1 and Statement 3: If all students are inquisitive (Statement 1), it is impossible for no student to be inquisitive (Statement 3). Thus, these two statements cannot be true at the same time.
• Statement 1 and Statement 2: Statement 2 is a weaker statement compared to Statement 1. If all students are inquisitive, then certainly some students are inquisitive, making these two statements compatible.
• Statement 2 and Statement 4: If some students are inquisitive (Statement 2), it is possible that some students are not inquisitive, making these two statements possible simultaneously.
• Statement 3 and Statement 4: If no student is inquisitive (Statement 3), it definitely includes some students are not inquisitive, thus these two statements are compatible.

Thus, the correct answer is: Statement 1 and Statement 3 cannot be true simultaneously.