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GATE CSE 2022 Q4: Two statements about inquisitive students that cannot both be true

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.

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 1/3 mark in GATE.
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Answer: A (official GATE 2022 final answer key)

Concept used: Square of opposition: contraries (All are / None are) cannot both be true when the class is non-empty.

First step: With at least one student, check which pair would force that student to be both inquisitive and not inquisitive.

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Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key

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