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.

Statements:

All walnuts are keys.

No walnut is a sun.

All suns are apples.

Conclusions:

(I): No apple is a key.

(II): Some apples are walnuts

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  1.  Only conclusion (II) follows.
  2. Both conclusions (I) and (II) follow.
  3. Only conclusion (I) follows.
  4. Neither conclusion (I) nor (II) follows.

Answer (Detailed Solution Below)

Option 4 : Neither conclusion (I) nor (II) follows.
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Detailed Solution

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Given Statements:

All walnuts are keys.

No walnut is a sun.

All suns are apples.

The Venn diagram for the given statements is:

Conclusions:

Conclusion I: No apple is a key.: False (There is no direct relation between apple and key so we cannot definitively say that no apple is a key.)

Conclusion II: Some apples are walnuts.: False (There is no direct relation between apple and walnuts so we cannot definitively say that Some apples are walnuts.)

So, neither conclusion I nor conclusion II follows.

Hence, the correct answer is "Option 4"

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