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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 engines are rockets. All planes are rockets. Conclusions: (I) Some engines are planes. (II) All planes are engines.
Only conclusion (II) follows
Both conclusions (I) and (II) follow
Only conclusion (I) follows
Neither conclusion (I) nor (II) follows
Neither conclusion (I) nor (II) follows
Draw standard overlapping Venn diagram or use middle term elimination. Since 'rockets' is middle term with 'All', no direct universal affirmative relation can be established between 'engines' and 'planes'.
Draw standard overlapping Venn diagram or use middle term elimination. Since 'rockets' is middle term with 'All', no direct universal affirmative relation can be established between 'engines' and 'planes'.
Analyze Statement 1
All engines are rockets means the set of Engines (E) is completely enclosed within the set of Rockets (R).
Analyze Statement 2
All planes are rockets means the set of Planes (P) is also completely enclosed within the set of Rockets (R).
Evaluate Conclusions
Both Engines and Planes lie inside Rockets, but their mutual relationship is not defined. Thus, neither 'Some engines are planes' nor 'All planes are engines' necessarily follows.
A: Only conclusion (II) follows is incorrect because planes and engines have no guaranteed overlap. B: Both conclusions follow is incorrect as neither can be definitively deduced. C: Only conclusion (I) follows is incorrect for the same reason.
D is correct because neither conclusion logically follows from the given statements since no direct relationship between engines and planes is established.
In syllogisms where two different subjects are subsets of the same universal set, do not assume any intersection between them unless explicitly stated or linked.
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