Question

Residency is a famous housing complex with many well-established individuals among its residents.
A survey revealed:
1. All residents who are well established in their respective fields are academicians.
2. Most of these academicians are authors of some best-selling books.
Based only on this information, which one of the following statements can be logically inferred with {certainty}?

• A. Some residents of the complex who are well established in their fields are also authors of some best-selling books.
• B. All academicians residing in the complex are well established in their fields.
• C. Some authors of best-selling books are residents of the complex who are well established in their fields.
• D. Some academicians residing in the complex are well established in their fields.

Hint:

When solving inference problems, carefully check whether the premises guarantee {existence}. Universal statements like “All X are Y” do not imply that X exists; you need explicit evidence to assert existence.

Answer 1

The Correct Option is A

Step 1: Translate the statements into logic form.
- Premise 1: If a resident is well established $\Rightarrow$ that resident is an academician.
- Premise 2: Most of these academicians (who are well established) are authors of best-selling books.
Step 2: Analyze each option.
(A) “Some well-established residents are also authors of best-selling books.”
Since most of the well-established residents (who are academicians) are authors, at least some must certainly be authors. $\Rightarrow$ This follows with certainty. (B) “All academicians are well established.”
This is not guaranteed. Premise 1 only says all well-established are academicians, but not all academicians are necessarily well established. (C) “Some authors of best-selling books are well-established residents.”
The survey only states that most of the well-established academicians are authors. But it does not confirm that any of these authors are residents of the complex outside this group. Cannot infer with certainty. (D) “Some academicians are well established.”
The premise says all well-established are academicians, but it does not guarantee that there exists even one well-established resident in the first place. The statement requires existence, which is not certain.
Step 3: Conclusion.
The only statement guaranteed true is (A). Final Answer: \[ \boxed{A} \]