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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 planets are rocks. All rocks are forests. Conclusions: (I) At least some rocks are planets. (II) All planets are forests.
Neither conclusion I nor II follows
Only conclusion II follows
Only conclusion I follows
Both conclusions I and II follow
Both conclusions I and II follow
Visualize Venn diagram: Planets are inside Rocks, and all Rocks are inside Forests. This implies all Planets are necessarily inside Forests.
Visualize Venn diagram: Planets are inside Rocks, and all Rocks are inside Forests. This implies all Planets are necessarily inside Forests.
Analyze Statement Relationships
From the statements: 1) All planets are rocks (Planets subset of Rocks). 2) All rocks are forests (Rocks subset of Forests). Thus, Planets are a subset of Rocks, which is a subset of Forests.
Evaluate Conclusions
Conclusion I: 'At least some rocks are planets' is true because all planets are rocks, which means some rocks must be planets. Conclusion II: 'All planets are forests' is true because the set 'Planets' is contained entirely within 'Rocks', which is contained entirely within 'Forests'.
A: Incorrect because it excludes conclusion I. B: Incorrect because it excludes conclusion II. C: Incorrect because it excludes conclusion II.
D is correct because both conclusions logically follow from the given premises: 'some rocks are planets' is the converse of the universal affirmative, and 'all planets are forests' is the transitive result of the two statements.
In Syllogism questions with all positive statements, check for the transitive property: if A is B and B is C, then A is C. Always remember that 'All' implies 'Some' is also true.
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