Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of these academicians are authors of some best-selling books.
Based only on the information provided above, which one of the following statements can be logically inferred with certainty?
Residency Complex Logic Puzzle
Premises Recap
- Fact 1: If a resident is well-established (WE), then they are an academician (AC). This means the set of well-established residents is a subset of the academicians. (WE ⊆ AC)
- Fact 2: Most academicians who are well-established (i.e., members of WE) are authors (BS). This directly implies that some well-established residents are authors. (WE ∩ BS ≠ ∅)
Analyzing Options
- Option 1: "Some residents of the complex who are well established in their fields are also authors of some best-selling books." This translates to "Some WE are BS". This is a direct and certain inference from Fact 2. This is the correct inference.
- Option 2: "All academicians residing in the complex are well established in their fields." This implies (AC ⊆ WE). Fact 1 states the reverse (WE ⊆ AC), so this cannot be inferred.
- Option 3: "Some authors of best-selling books are residents of the complex who are well established in their fields." This translates to "Some BS are WE". This is logically equivalent to Option 1 and also derivable from Fact 2.
- Option 4: "Some academicians residing in the complex are well established in their fields." This implies (Some AC are WE). Fact 1 (WE ⊆ AC) does not guarantee that any residents *are* well-established (WE might be an empty set). Therefore, this cannot be inferred with certainty.
The inference that aligns perfectly and certainly with the provided statements is that some well-established residents are authors.
Important Questions from Logical Deduction
- The following observation is made about the scores obtained by 100 students in an exam:
'For each student, there exists another student in the class such that their scores are at most ten marks away.'
If the above statement is false, which one of the following statements is necessarily true? - Consider the following two phonological rules:
Rule 1: Vowel Epenthesis of [ɪ] after sibilant-ending stems
Rule 2: Progressive Voicing Assimilation of the plural affix
Which ONE of the following rule ordering relations apply in the case of regular English pluralization as in ‘horse’ – ‘horses’? Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules:
- Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON.
- Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
- The state of any bulb not meeting the conditions above is left unchanged.
The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.
The number of bulbs which are ON at the end of Step 8 is ______
- Based only on the conversation below, identify the logically correct inference:
“Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine. Consider a five-digit number PQRST that has distinct digits P, Q, R, S and T, and satisfies the following conditions:
$P < Q$
$S > P > T$
$R < T$
If integers 1 through 5 are used to construct such a number, the value of P is:
