Question

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

Accepted Answer

D. 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.

Syllogisms and Subalternation Statements

Explanation

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