Project ForgeGiven 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
- BStatement 1 and Statement 2
- CStatement 2 and Statement 4
- DStatement 3 and Statement 4
Explanation
Statement 1 ('All are inquisitive') and Statement 3 ('No student is inquisitive') are direct 'contraries' in the square of opposition — with at least one student existing, these are mutually exclusive extremes that can never both hold at once (though they COULD both be false, e.g. if some but not all are inquisitive). Statements 2 and 4 ('some are' / 'some are not') are 'subcontraries' — they CAN both be true simultaneously (a mixed class), so they don't qualify.
Source: GATE CS 2022 (2022)
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