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Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements. Statements: All schools are colleges. No college is a university. Conclusions: (I) Some colleges are not schools. (II) Some schools may be universities.
Neither conclusion I nor II follows
Only conclusion II follows
Only conclusion I follows
Both conclusions I and II follow
Only conclusion I follows
Use Venn diagrams: 'All A are B' means circle A is inside B. 'No B is C' means B and C never touch. If A is inside B, and B cannot touch C, then A also cannot touch C.
Use Venn diagrams: 'All A are B' means circle A is inside B. 'No B is C' means B and C never touch. If A is inside B, and B cannot touch C, then A also cannot touch C.
Analyze the Statements
Statement 1: All schools are colleges (Schools are a subset of Colleges). Statement 2: No college is a university (Colleges and Universities are disjoint sets).
Evaluate Conclusion I
Conclusion I: Some colleges are not schools. Since all schools are colleges, we know there are colleges that are definitely schools, but the information does not force some colleges to exist outside the 'school' circle. Thus, this is not necessarily true.
Evaluate Conclusion II
Conclusion II: Some schools may be universities. Since all schools are within the 'college' circle, and no college can be a university, it is impossible for any school to be a university. This conclusion is false.
A: Only I follows is incorrect because I is not necessarily true. B: Both conclusions follow is incorrect because II is definitely false. D: Only conclusion II follows is incorrect because II is definitely false.
C is correct because neither of the conclusions follows logically from the given statements based on set theory.
In Syllogism, remember that 'No A is B' establishes a negative link that flows through the entire hierarchy (if all C are A, then no C is B).
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