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 students are teachers.
All teachers are professors.
Conclusions:
1. All students are professors.
2. All professors are students.
3. No teacher is a professor.

Question

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 students are teachers.

All teachers are professors.

Conclusions:

1. All students are professors.

2. All professors are students.

3. No teacher is a professor.

Prepp Team · Accepted Answer

Solving Syllogism Questions: Statements and Conclusions

Syllogism questions test your ability to derive logical conclusions from given statements. The key is to assume the statements are true, regardless of real-world facts, and determine what strictly follows.

Understanding the Given Syllogism Statements

Let's break down the provided statements:

Statement 1: Some goats are eagles. (This indicates a partial overlap between the category of Goats and the category of Eagles.)
Statement 2: All eagles are snakes. (This means the category of Eagles is entirely contained within the category of Snakes.)
Statement 3: No duck is an eagle. (This indicates a complete separation between the category of Ducks and the category of Eagles.)

Analyzing the Syllogism Conclusions

Now, let's evaluate each conclusion based on the given statements:

Conclusion (I): No snake is a goat.

From Statement 1, we know that 'Some goats are eagles'. From Statement 2, we know that 'All eagles are snakes'. If some goats are eagles, and all eagles are snakes, then those specific goats that are eagles must also be snakes. Therefore, it logically follows that 'Some goats are snakes'.

Since 'Some goats are snakes' is a definite consequence of the statements, the conclusion 'No snake is a goat' is false. Conclusion I does not follow.

Conclusion (II): Some ducks are snakes is a possibility.

From Statement 3, we know 'No duck is an eagle'. From Statement 2, 'All eagles are snakes'. This tells us that Ducks and Eagles are separate, and Eagles are part of Snakes.

The statements don't provide a direct relationship between Ducks and Snakes, other than the fact that Ducks cannot be in the 'Eagle' portion of Snakes. However, Ducks could potentially overlap with the 'non-eagle' portion of Snakes. There is no statement that prohibits Ducks from being snakes. Therefore, a situation where 'Some ducks are snakes' is possible.

Conclusion II follows as a possibility.

Conclusion (III): Some ducks are not goats.

We know 'No duck is an eagle' and 'Some goats are eagles'. There is no direct relationship given between Ducks and Goats. We can draw possible scenarios (using Venn diagrams mentally or on paper) for the relationship between Ducks and Goats:

Scenario A: Some ducks are goats, and some ducks are not goats. (In this case, Conclusion III is true).
Scenario B: No ducks are goats. (In this case, Conclusion III is true - all ducks are not goats, which implies some are not).
Scenario C: All ducks are goats. (In this case, Conclusion III 'Some ducks are not goats' is false).

Since we can construct a scenario where 'Some ducks are not goats' is false (Scenario C), this conclusion does not definitely follow from the statements. It might be true, but it's not guaranteed by the logic.

Conclusion III does not definitely follow.

Summary of Conclusions

Conclusion (I) does not follow.
Conclusion (II) follows as a possibility.
Conclusion (III) does not definitely follow.

Based on this analysis, only conclusion II logically follows (as a possibility) from the given statements.

Conclusion	Analysis	Follows?
(I) No snake is a goat.	Statements imply "Some goats are snakes".	No
(II) Some ducks are snakes is a possibility.	Ducks are separate from Eagles, but can overlap with the rest of Snakes.	Yes (as a possibility)
(III) Some ducks are not goats.	Relationship between Ducks and Goats is not defined; a scenario exists where all ducks are goats.	No (not definitely)

Revision Table: Key Syllogism Concepts

Concept	Description
Statement Validity	Always assume given statements are true, even if unrealistic.
Logical Follows	A conclusion logically follows if it MUST be true whenever the statements are true.
Possibility	A conclusion follows as a possibility if it MIGHT be true without contradicting the statements.
Venn Diagrams	Useful tool to visually represent categories and their relationships from statements.

Additional Information: Types of Syllogism Statements

Syllogism statements typically fall into four types:

All A are B: Universal Affirmative. The entire category A is included in category B. (e.g., All eagles are snakes).
No A is B: Universal Negative. Category A and category B are completely separate. (e.g., No duck is an eagle).
Some A are B: Particular Affirmative. There is at least one element common to both categories A and B. (e.g., Some goats are eagles).
Some A are not B: Particular Negative. There is at least one element in category A that is not in category B.

Understanding these statement types helps in correctly interpreting the relationships and drawing conclusions in syllogism problems.

Prepp Team · Answer

Both conclusions II and III follow

Prepp Team · Answer

Only conclusion III follows

Prepp Team · Answer

Both conclusions I and II follow