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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 museums are parks. No park is a theatre. Conclusions: (I) No museum is a theatre. (II) At least some parks are museums.
Only conclusion I follows
Both conclusions I and II follow
Neither conclusion I nor II follows
Only conclusion II follows
Both conclusions I and II follow
Represent 'All A are B' as an inner circle (A) inside outer (B), and 'No B is C' as a separate circle (C) that cannot touch (B). If A is in B, it cannot touch C.
Represent 'All A are B' as an inner circle (A) inside outer (B), and 'No B is C' as a separate circle (C) that cannot touch (B). If A is in B, it cannot touch C.
Analyze Statement 1
All museums are parks. This means the set of museums is entirely contained within the set of parks.
Analyze Statement 2
No park is a theatre. Since museums are inside parks, museums also cannot have any intersection with the set of theatres.
Evaluate Conclusions
Conclusion I: 'No museum is a theatre' is True, as museums are contained in parks, and parks have no intersection with theatres. Conclusion II: 'At least some parks are museums' is the converse of 'All museums are parks' and is always true if the original statement is true.
A: Wrong, both follow. C: Wrong, both follow. D: Wrong, both follow.
B is correct because the logical containment of museums within parks and the exclusion of parks from theatres necessarily forces both conclusions to be true.
In Syllogism, always remember that 'All A are B' inherently means 'Some B are A'. Also, if A is inside B, and B is excluded from C, then A is automatically excluded from C.
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