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
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.
The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow (s) from the information given in the statements.
Statements:
All books are grapes.
Some grapes are fruits.
Conclusions:
I. No grape is a book.
II. Some grapes are books.The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some fans are radio.
All fans are light.
Conclusion I: Some radios are light.
Conclusion II: Some lights are radio.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 scissors are spoons.
All spoons are plates.
Conclusions:
1. Some plates are spoons.
2. Some spoons are scissors.
3. Some plates are scissors.
Read the given statements and conclusions carefully. Assuming that the information given in the statement 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 boat is ship.
Some ships are rods.
Conclusions:
I. No boat is rod.
II. Some rods are ships.
III. Some rods are not boats.
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 bottles are glasses.
All glasses are jugs.
Conclusions:
I. All bottles are jugs.
II. All jugs are bottles.
III. Some glasses are bottles.
In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some pen are black.
II. Some pen are blue.
III. No black is red.
Conclusions:
I. No pen is red.
II. Some blue are black.
III. Some black are pens.In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All cups are plates.
II. All plates are red.
Conclusions:
I. All cups are red.
II. All plates are cups.
III. All red are plates.In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some sky are blue.
II. Some blue are soft.
Conclusions:
I. Some sky are soft.
II. Some soft are sky.What will come in the place of the question mark (?) in the following equation if '+' and '-' are interchanged and 'x' and '÷' are interchanged?
108 × 2 − 14 ÷ 6 + 27 = ?
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
