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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 bees are insects. All bees are hives. Conclusions: (I) Some hives are insects. (II) All hives are bees.
Only conclusion (II) follows
Only conclusion (I) follows
Neither conclusion (I) nor (II) follows
Both conclusions (I) and (II) follow
Only conclusion (I) follows
For syllogisms involving 'All A are B' and 'All A are C', A is the common subject; therefore, the intersection of B and C is at least A, making 'Some C are B' always true.
For syllogisms involving 'All A are B' and 'All A are C', A is the common subject; therefore, the intersection of B and C is at least A, making 'Some C are B' always true.
Analyze Statement 1 and 2
All bees are insects (Bees subset of Insects) and all bees are hives (Bees subset of Hives). Both sets 'Insects' and 'Hives' contain the set 'Bees'.
Evaluate Conclusion (I)
Since all bees are insects and all bees are hives, there exists a group (bees) that is part of both insects and hives. Therefore, 'Some hives are insects' must be true.
Evaluate Conclusion (II)
The statement 'All bees are hives' does not imply the reverse. 'Some hives are bees' is true, but 'All hives are bees' is not necessarily true, as there could be hives that are not bees.
A: Only (II) is incorrect because 'All hives are bees' is not supported by the premises. C: Neither is incorrect because (I) is clearly logically derived from the intersection. D: Both is incorrect because the universal affirmation 'All hives are bees' cannot be inferred from 'All bees are hives'.
B is correct because the common overlap of 'Bees' within both 'Insects' and 'Hives' guarantees that some hives are insects, while the reverse containment of all hives within bees is logically invalid.
Always remember that All A is B does not mean All B is A. When two subjects share a common predicate, 'Some' relations between those predicates are always valid.