Statements:
Some birds are eagles.
All eagles are fierce.
All fierce creatures are predators.
Conclusions:
(1) Some birds are fierce.
(2) Some birds are predators.
(3) All predators are fierce.
(4) No eagle is a predator.
Analyzing the Statements: Birds, Eagles, and Predators
This question tests our ability to use deductive reasoning based on a set of given statements. We need to carefully examine each statement and conclusion to see if the conclusion logically follows from the statements alone. Let's break down the provided information.
Provided Statements
- Statement 1: Some birds are eagles.
- Statement 2: All eagles are fierce.
- Statement 3: All fierce creatures are predators.
Evaluating Each Conclusion
Conclusion (1): Some birds are fierce.
We start with Statement 1: "Some birds are eagles." This means there is at least one bird that is also an eagle.
Next, we look at Statement 2: "All eagles are fierce." This tells us that every single eagle possesses the quality of being fierce.
Combining these two statements:
- If there exists at least one bird that is an eagle (from S1),
- And every eagle is fierce (from S2),
- Then it must be true that at least one bird (the one that is an eagle) is also fierce.
Therefore, Conclusion (1) logically follows from Statements 1 and 2.
Conclusion (2): Some birds are predators.
From our analysis of Conclusion (1), we established that "Some birds are fierce."
Now, let's consider Statement 3: "All fierce creatures are predators." This means that anything described as fierce also belongs to the category of predators.
Combining the established fact ("Some birds are fierce") with Statement 3:
- If there exists at least one bird that is fierce (derived from S1 & S2),
- And every fierce creature is a predator (from S3),
- Then it must be true that at least one bird (the one that is fierce) is also a predator.
Therefore, Conclusion (2) logically follows from the statements.
Conclusion (3): All predators are fierce.
Statement 3 says: "All fierce creatures are predators." This means the group of fierce creatures is entirely contained within the larger group of predators. We can represent this as: Fierce \(\subset\) Predators.
The conclusion states: "All predators are fierce." This would mean the group of predators is entirely contained within the group of fierce creatures (Predators \(\subset\) Fierce).
Statement 3 does not provide information that allows us to conclude the reverse is true. There might be predators that are not fierce. We cannot assume the relationship works both ways just because one direction is stated.
Therefore, Conclusion (3) does not logically follow.
Conclusion (4): No eagle is a predator.
Let's revisit the connections:
- From Statement 2: All eagles are fierce.
- From Statement 3: All fierce creatures are predators.
If all eagles are fierce, and all fierce creatures are predators, then it must logically follow that all eagles are predators. This is a transitive property.
The conclusion "No eagle is a predator" directly contradicts this derived fact.
Therefore, Conclusion (4) does not logically follow.
Final Determination
Based on the step-by-step analysis:
- Conclusion (1) follows.
- Conclusion (2) follows.
- Conclusion (3) does not follow.
- Conclusion (4) does not follow.
The only conclusions that logically follow from the given statements are (1) and (2).
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.
