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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 belts are watches. No belt is a tie. Conclusions: (I) No watch is a tie. (II) At least some watches are belts.
Only conclusion I follows
Only conclusion II follows
Neither conclusion I nor II follows
Both conclusions I and II follow
Only conclusion II follows
Visualize Venn diagram: Belt is inside Watch; No overlap between Belt and Tie. This implies No Watch is Tie is NOT necessarily true (a Watch can contain a Tie as long as it's not the Belt part), but some Watches are definitely Belts.
Visualize Venn diagram: Belt is inside Watch; No overlap between Belt and Tie. This implies No Watch is Tie is NOT necessarily true (a Watch can contain a Tie as long as it's not the Belt part), but some Watches are definitely Belts.
Analyze Statement 1
All belts are watches means the set of Belts is entirely contained within the set of Watches.
Analyze Statement 2
No belt is a tie means the sets Belts and Ties are mutually exclusive (no overlap).
Evaluate Conclusions
Conclusion I: No watch is a tie. This is not necessarily true because the 'Watch' set could overlap with 'Tie' in areas where there are no 'Belts'. Conclusion II: At least some watches are belts. This is logically true because 'All belts are watches' implies at least one belt exists as a watch.
A: Only conclusion I is wrong because 'No watch is a tie' is not definitive; C: Neither follows is wrong as II is valid; D: Both follow is wrong as I is not definitively true.
B is correct because the statement 'All belts are watches' directly confirms that those belts are indeed watches (making some watches belts), whereas 'No watch is a tie' cannot be confirmed because the restriction only applies to belts.
In Syllogism, remember that 'All A are B' always guarantees 'Some B are A'. Always check for the possibility of overlapping sets unless explicitly restricted.
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