Humpty Dumpty sits on a wall every day while having lunch. The wall sometimes breaks. A person sitting on the wall falls if the wall breaks.
Which one of the statements below is logically valid and can be inferred from the above sentences?
Logical Inference Analysis: Humpty Dumpty
Analyze the given statements to find the logically valid inference.
Premises Analysis
- Humpty Dumpty eats lunch on a wall daily.
- The wall sometimes breaks.
- If the wall breaks while Humpty Dumpty is on it, he falls.
Option Evaluation
- Option 1: Humpty Dumpty always falls while having lunch
The wall breaks sometimes, not always. Therefore, Humpty Dumpty does not always fall. This is invalid. - Option 2: Humpty Dumpty does not fall sometimes while having lunch
Since the wall sometimes breaks, it means the wall sometimes does not break. According to premise 3, if the wall does not break, Humpty Dumpty does not fall. Thus, he sometimes does not fall. This is a valid inference. - Option 3: Humpty Dumpty never falls during dinner
The provided text only discusses lunch. There is no information about dinner. This is invalid. - Option 4: When Humpty Dumpty does not sit on the wall, the wall does not break
The text states the wall breaks *while* he sits on it, but it does not specify what happens when he is absent. The wall could still break. This is invalid.
The only logically valid inference is that Humpty Dumpty sometimes does not fall.
Important Questions from Logical Inferences
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 IndiaIn 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?
