Question 33

Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statement I: No food is water.
Statement II: All food are snacks.
Conclusion I: No water is a snack.
Conclusion II: All water can be snacks.

Convert the two statements into standard set‐language.

Statement I: “No food is water”  ⇒  $$Food \cap Water = \varnothing$$.

Statement II: “All food are snacks”  ⇒  $$Food \subseteq Snacks$$.

Draw an Euler/Venn picture that respects both conditions: place the circle Food completely inside Snacks and completely outside Water. Apart from that, the relative position of Water and Snacks is unrestricted; Water might overlap Snacks or might lie wholly outside it.

Now test each conclusion.

Conclusion I: “No water is a snack”  ⇒  $$Water \cap Snacks = \varnothing$$.
This would force the circles Water and Snacks to be disjoint. But our diagram shows it is perfectly permissible for Water to overlap Snacks (because only Food is prohibited from touching Water). Since the conclusion is not inevitable, Conclusion I does not follow.

Conclusion II: “All water can be snacks” means “It is possible that $$Water \subseteq Snacks$$ without violating the given statements.” Such a placement is indeed possible: put the entire Water circle inside Snacks but ensure it does not touch Food (already disjoint by Statement I). Because this arrangement satisfies both original statements, the possibility asserted in Conclusion II is logically valid. Hence Conclusion II follows.

Therefore, only Conclusion II follows from the given statements.

Option C which is: Only II follows

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