Discussion
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.
Answer: A
The two statements that cannot both be true are Statement 1 and Statement 3.
'All students are inquisitive' and 'No student is inquisitive' are contraries: with at least one student in the class, that student would have to be both inquisitive and not inquisitive.
The other pairs can hold together. If all students are inquisitive, then some students are inquisitive too, so 1 and 2 are compatible. 'Some are' and 'some are not' are both true in a mixed class, so 2 and 4 are compatible. If no student is inquisitive, then certainly some students are not, so 3 and 4 are compatible.
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