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

Step 1: Analyze the Statements.
- Statement 1: All students are inquisitive.
This statement asserts that every student is inquisitive, so it is a universal positive statement.
- Statement 2: Some students are inquisitive.
This statement asserts that at least one student is inquisitive, which is a partial positive statement. It is logically consistent with Statement 1.
- Statement 3: No student is inquisitive.
This statement asserts that no student is inquisitive, which directly contradicts Statement 2 and Statement 1.
- Statement 4: Some students are not inquisitive.
This statement asserts that at least one student is not inquisitive, which is logically consistent with Statement 2.
Step 2: Identify the contradictory statements.
Statements 1 and 3 cannot both be true at the same time. If all students are inquisitive (Statement 1), then no student can be inquisitive (Statement 3) is a contradiction. Therefore, Statements 1 and 3 cannot both be true simultaneously.
Step 3: Conclusion.
The correct answer is (A) Statement 1 and Statement 3.