Understanding the Logic Puzzle
This question asks us to determine a valid conclusion based on two given statements (premises) about humans, immortality, and scientists.
Analyzing the Premises
- Premise 1: No humans are immortal.
- This means that every human being is mortal. If someone is human, they cannot be immortal.
- We can represent this using sets: Let H be the set of Humans and I be the set of Immortals. Then, the premise states that the intersection of these sets is empty: \(H \cap I = \emptyset\).
- Alternatively, we can say all humans belong to the set of mortal beings.
- Premise 2: Some humans are scientists.
- This means there is at least one person who is both a human and a scientist.
- Using sets: Let S be the set of Scientists. This premise states that the intersection of H and S is not empty: \(H \cap S \neq \emptyset\).
Evaluating the Options
Let's examine each option to see if it logically follows from the premises:
- Option 1: All humans are immortal
- This directly contradicts Premise 1 ("No humans are immortal"). Therefore, this option is incorrect.
- Option 2: All scientists are mortal
- We know from Premise 2 that some scientists are humans. We also know from Premise 1 that all humans are mortal. So, those scientists who are humans must be mortal.
- However, Premise 2 only says "Some humans are scientists," not "All scientists are humans." There could be scientists who are not human. The premises do not give us any information about the mortality of non-human scientists.
- Therefore, we cannot conclude that *all* scientists are mortal. This option is not necessarily true.
- Option 3: Some scientists are not immortal
- From Premise 2, we know there exist individuals who are both human and scientists. Let's call one such individual 'Alex'.
- So, Alex is a human (\(Alex \in H\)) and Alex is a scientist (\(Alex \in S\)).
- From Premise 1, we know that no human is immortal (\(H \cap I = \emptyset\)). Since Alex is human (\(Alex \in H\)), Alex cannot be immortal (\(Alex \notin I\)).
- Since Alex is a scientist (\(Alex \in S\)) and Alex is not immortal (\(Alex \notin I\)), it means there is at least one scientist (Alex) who is not immortal.
- This perfectly matches the statement "Some scientists are not immortal". This conclusion is logically valid.
- Option 4: Some scientists are not humans
- Premise 2 states "Some humans are scientists." This implies the group of scientists and the group of humans have some overlap.
- It does *not* provide any information about whether there are scientists who fall *outside* the human group. While it might be true in reality, we cannot logically deduce it *solely* from the given premises.
- Therefore, this option is not necessarily true based on the given information.
Final Conclusion
Based on the logical analysis of the premises, the only conclusion that must be true is that some scientists are not immortal.
Similar Questions
- All flowers are plants. Some plants are flowering plants. Which conclusion is logically valid?
Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known f act s, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some carpenters are singers.
All singers are doctors.
Conclusions:
I. No doctor is a carpenter.
II. Some doctors are singers.
III. Some carpenters are doctors.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statement s to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some machines are coolers.
All coolers are robots.
Some microwaves are coolers.
Conclusions:
I. Some coolers are machines.
II. Some robots are machines.
III. No robot is a microwave.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. All teachers are students.
2. All principal are teachers.
3. Some principals are doctors.
Conclusions:
I. Some students are teachers.
II. No student is a doctor.
III. Some students are principals.Two statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. All apples are mangoes.
2. Some bananas are mangoes.
Conclusions:
I. Some mangoes are bananas.
II. Some mangoes are apples.
III. No mango is an apple.Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. No bed is a chair.
2. All tables are beds.
3. No cupboard is a bed.
Conclusions:
I. No table is a chair.
II. No cupboard is a table.
III. Some beds are tables.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. No city is a district.
2. Some districts are zones.
3. Some zones are states.
Conclusions:
I. Some zones are districts.
II. Some districts are cities.
lII. No state is a zone.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. Some tables are chairs.
2. Some chairs are beds.
3. All beds are goods.
Conclusions:
I. Some chairs are goods.
Il. Some goods are not beds.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
No man is engineer.
No engineer is driver.
Some drivers are shop-keepers.
Conclusions:
1. Some men are drivers.
2. No shop-keepers are engineer.
3. Some shop-keepers are not engineers.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All aero-planes are cars.
All helicopters are cars.
All cars are scooters.
Conclusions:
1. All helicopters are scooters.
2. Some aero-planes are helicopters.
3. No aero-plane is helicopter.
Important Questions from Syllogism
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
