Question

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 inks are pens.

All pens are rubbers.

No rubber is a sharpener.

Conclusions:

(I) No ink is a sharpener.

(Il) Some rubbers are inks.

• A. Both conclusions (I) and (II) follow
• B. Neither conclusion (I) nor (II) follows
• C. Only conclusion (II) follows
• D. Only conclusion (I) follows

Answer 1

Answer:

A. Both conclusions (I) and (II) follow

Both conclusions (I) and (II) logically follow from the given statements.

We can analyze this using a Venn diagram approach:

• "All inks are pens" means the circle for "inks" is completely inside the circle for "pens".

• "All pens are rubbers" means the circle for "pens" (which already contains "inks") is completely inside the circle for "rubbers".

• "No rubber is a sharpener" means the circle for "rubbers" is completely separate from the circle for "sharpener".

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Evaluating the Conclusions

• Conclusion (I): No ink is a sharpener.

  • True. Since the entire "rubber" circle is separated from "sharpener", anything inside the "rubber" circle (which includes all "inks") can never touch or be a "sharpener".

• Conclusion (II): Some rubbers are inks.

  • True. Since all "inks" are inside the "rubbers" circle, that specific part of the "rubbers" circle is occupied by "inks". Therefore, some rubbers are definitely inks.

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Both conclusions (I) and (II) follow.