Assume that the following three statements are true:
(A) All freshmen are human
(B) All students are human
(C) Some students think
Given the following four statements:
(I) All freshmen are students
(II) Some humans think
(III) No freshmen think
(IV) Some humans who think are not students
Those which are logical consequences of A, B, and C are:
Explanation
Solution
1. Analysis of Conclusions:
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Conclusion (I): Freshmen and Students are both subsets of Humans. No direct link exists between them. ⇒ False
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Conclusion (II): Since All Students ⊆ Humans and Some Students ∩ Thinkers =ϕ, then Some Humans ∩ Thinkers =ϕ. ⇒ True
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Conclusion (III): No relationship is established between Freshmen and the act of thinking. ⇒ False
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Conclusion (IV): We only know some students think; we cannot confirm the existence of thinking humans who are not students. ⇒ False
2. Final Result:
Only statement II is a logical consequence.
Correct Option: (a) II