Syllogisms and Subalternation Statements
CMAT 2023 · Logical Reasoning · Medium · Syllogisms
Given below are two statements : Statement I: If 'some students are intelligent' is true, then 'some students are not intelligent' is also true. Statement II: If 'all logicians are mathematician' is true, then 'some non-mathematicians are not logicians' will be true. In the light of the above statements, choose the correct answer from the options given below.
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is true but Statement II is false
- D.
Statement I is false but Statement II is true
D
Explanation
Statement I: 'Some A are B' being true does NOT logically guarantee 'Some A are not B' (all A could be B). So Statement I is false. Statement II: 'All L are M' means all non-M are non-L. Thus no non-mathematician is a logician, which implies 'some non-mathematicians are not logicians'. So Statement II is true.
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