Based on the statements in (1) – (4), which option/s is/are correct?
(1) Thor has a female sibling
(2) Thor has a sister
(3) Thor has visited New Delhi
(4) Thor has visited India
Statement Relationship Analysis
We need to determine the logical entailment between the given statements about Thor.
- Statements (1) and (2):
- (1) Thor has a female sibling.
- (2) Thor has a sister.
A "sister" is specifically a female sibling. Therefore, if Thor has a sister (2), he necessarily has a female sibling (1). So, (2) entails (1).
Conversely, a "female sibling" is definitionally a "sister". If Thor has a female sibling (1), then that sibling is his sister (2). So, (1) entails (2).
Conclusion: Statements (1) and (2) are logically equivalent; (1) entails (2) and (2) entails (1).
- Statements (3) and (4):
- (3) Thor has visited New Delhi.
- (4) Thor has visited India.
New Delhi is a major city located within India. If Thor has visited New Delhi (3), it logically follows that he must have visited India (4). So, (3) entails (4).
However, visiting India (4) does not guarantee visiting New Delhi (3). Thor could have visited other cities in India (e.g., Mumbai, Kolkata) without visiting New Delhi. So, (4) does not entail (3).
Option Evaluation
Based on the analysis above, let's evaluate the given options:
- Option A: (1) entails (2); (3) entails (4)
- (1) entails (2) is TRUE.
- (3) entails (4) is TRUE.
Therefore, Option A is correct.
- Option B: (2) entails (1); (4) does not entail (3)
- (2) entails (1) is TRUE.
- (4) does not entail (3) is TRUE.
Therefore, Option B is correct.
- Option C: (1) does not entail (2); (3) does not entail (4)
- (1) does not entail (2) is FALSE.
- (3) does not entail (4) is FALSE.
Therefore, Option C is incorrect.
- Option D: (2) does not entail (1); (4) entails (3)
- (2) does not entail (1) is FALSE.
- (4) entails (3) is FALSE.
Therefore, Option D is incorrect.
Conclusion
The analysis confirms that both Option A and Option B accurately describe the logical relationships between the statements.
Important Questions from Logical Inferences
In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.
When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.
Based only on the above information, which one of the following statements can be logically inferred with certainty?Elvesland is a country that has peculiar beliefs and practices. They express almost all their emotions by gifting flowers. For instance, if anyone gifts a white flower to someone, then it is always taken to be a declaration of one's love for that person. In a similar manner, the gifting of a yellow flower to someone often means that one is angry with that person.
Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?
(i) In Elvesland, one always declares one's love by gifting a white flower.
(ii) In Elvesland, all emotions are declared by gifting flowers.
(iii) In Elvesland, sometimes one expresses one's anger by gifting a flower that is not yellow.
(iv) In Elvesland, sometimes one expresses one's love by gifting a white flower.
- In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of the qualified candidates.
Which one of the following is the correct logical inference based on the information provided in the above passage? 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?
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?
