A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.
Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?
Survey Statistics for Inference
The question asks for a conclusion that can be logically inferred with certainty, based only on the provided survey data about tobacco use.
Key Survey Statistics
- Percentage of tobacco users advised to stop: 65%
- Proportion of tobacco users who attempted to stop: 3 out of 10, which equals 30%
Inference Options Evaluation
Let T be the total number of tobacco users surveyed.
Group A: Tobacco users advised to stop. The size of this group is $0.65T$.
Group B: Tobacco users who attempted to stop. The size of this group is $0.30T$.
We need to evaluate the statement: "A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so." This statement is true if the number of users who were advised but did NOT attempt to stop (let's call this group $A \setminus B$) is greater than 50% of the size of Group A.
Range Calculation for Non-Attempting Advised Users
The number of users who were both advised and attempted to stop is the intersection of Group A and Group B ($A \cap B$). The size of this intersection, $|A \cap B|$, can vary.
- The minimum possible overlap is 0 (if none of the 30% who attempted were among the 65% advised).
- The maximum possible overlap is the size of the smaller group, which is $0.30T$.
The number of advised users who did NOT attempt to stop is calculated as $|A \setminus B| = |A| - |A \cap B|$.
Considering the range of overlap:
- If the overlap is maximum ($|A \cap B| = 0.30T$): The number who did not attempt is $0.65T - 0.30T = 0.35T$.
- If the overlap is minimum ($|A \cap B| = 0$): The number who did not attempt is $0.65T - 0 = 0.65T$.
Therefore, the number of advised users who did not attempt to stop falls between $0.35T$ and $0.65T$.
Majority Condition Check
We need to determine if this number ($|A \setminus B|$) represents a majority (more than 50%) of Group A ($|A| = 0.65T$).
50% of Group A is $0.50 \times 0.65T = 0.325T$.
We check if the calculated range for $|A \setminus B|$ is greater than $0.325T$:
- The minimum value $0.35T$ is greater than $0.325T$.
- The maximum value $0.65T$ is also greater than $0.325T$.
Since even the minimum possible number of advised users who did not attempt ($0.35T$) constitutes more than 50% of the advised group ($0.325T$), this statement can be inferred with certainty.
Logical Conclusion from Data
Other options are not verifiable: Option 1 is incorrect because 30% (attempted) is not a majority of 65% (advised). Options 3 and 4 are incorrect because the survey provides data on advice given and attempts made, not successful cessation rates.
Therefore, the only statement that can be logically inferred with certainty is that a majority of tobacco users advised to stop did not attempt to do so.
Important Questions from Logical Inferences
- Which of the following statements about languages and dialects is/are CORRECT?
- A person has a plan to climb a hill to reach the hilltop. She observes that there is a sudden rise in the water level in the stream coming down from the hill. From this she concludes that it must be raining heavily on the hilltop. Therefore, she should postpone her expedition to some later time.
Which one or more of the following kinds of inference does this person’s reasoning involve as per the Nyāya view? - Identify the instance(s) of inductive reasoning from the following options.
Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time the due date for registration was over, it was found that suprisingly none of the students from the Department of Human Sciences had completed the registration process.
Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?
(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.
(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.
(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.A duck named Donald Duck says “All ducks always lie."
Based only on the information above, which one of the following statements can be logically inferred with certainty?
