In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements. Statements : All candies are gems. All gems are cakes. Some cakes are sweets. Conclusions : I. All candies are cakes. II. Some gems are sweets
Only conclusion I follows.
This question asks us to analyze given statements and determine which of the provided conclusions logically follow. This is a classic type of question in logical reasoning, specifically syllogism.
Understanding the Statements and Conclusions in Syllogism
We are given three statements and two conclusions:
- Statement 1: All candies are gems.
- Statement 2: All gems are cakes.
- Statement 3: Some cakes are sweets.
- Conclusion I: All candies are cakes.
- Conclusion II: Some gems are sweets.
In syllogism, we must assume the statements are true and use only these statements to evaluate the conclusions.
Analyzing Conclusion I: All candies are cakes
Let's look at the first two statements:
- All candies are gems.
- All gems are cakes.
We can combine these two statements. If all of something (candies) is part of a group (gems), and all of that group (gems) is part of an even larger group (cakes), then it logically follows that all of the first something (candies) must also be part of the largest group (cakes).
Think of it like nested categories:
- Candies are inside the group 'Gems'.
- Gems are inside the group 'Cakes'.
This structure directly implies that Candies are inside the group 'Cakes'.
Therefore, Conclusion I: "All candies are cakes" logically follows from the given statements.
Analyzing Conclusion II: Some gems are sweets
Now let's look at the statements relevant to Conclusion II, which links 'gems' and 'sweets':
- All gems are cakes. (Statement 2)
- Some cakes are sweets. (Statement 3)
Statement 2 tells us that the group 'Gems' is entirely contained within the group 'Cakes'. Statement 3 tells us that there is some overlap between the group 'Cakes' and the group 'Sweets'.
However, the overlap between 'Cakes' and 'Sweets' could be in the part of 'Cakes' that is *not* 'Gems'.
Consider these possibilities based on Statements 2 and 3:
- The portion of 'Cakes' that are 'Sweets' could be entirely outside the portion of 'Cakes' that are 'Gems'. In this case, no gems would be sweets.
- The portion of 'Cakes' that are 'Sweets' could partially overlap with the portion of 'Cakes' that are 'Gems'. In this case, some gems would be sweets.
- The portion of 'Cakes' that are 'Sweets' could entirely contain the portion of 'Cakes' that are 'Gems'. In this case, all gems would be sweets (which implies some gems are sweets).
Since possibility 1 (no gems are sweets) is consistent with the given statements, we cannot definitively conclude that "Some gems are sweets". A conclusion in syllogism must *necessarily* follow in all possible scenarios depicted by the statements.
Therefore, Conclusion II: "Some gems are sweets" does not logically follow from the given statements.
Summary of Conclusions
- Conclusion I: All candies are cakes. - Follows.
- Conclusion II: Some gems are sweets. - Does not follow.
Based on our analysis, only Conclusion I logically follows from the given statements.
Revision Table: Syllogism Rules Applied
| Statement Combination | Example | Valid Conclusion Type |
|---|---|---|
| All A are B + All B are C | All candies are gems + All gems are cakes | All A are C (e.g., All candies are cakes) |
| All B are C + Some C are D | All gems are cakes + Some cakes are sweets | No definite conclusion between B and D (e.g., between Gems and Sweets) |
Additional Information on Syllogism and Logical Deductions
Syllogism is a form of deductive reasoning where a conclusion is inferred from two or more statements (premises). The validity of the conclusion depends solely on the logical form of the statements, not on the truth of the statements in the real world.
Key types of statements in syllogism are:
- Universal Affirmative (A): All S are P (e.g., All cats are animals).
- Universal Negative (E): No S are P (e.g., No cats are dogs).
- Particular Affirmative (I): Some S are P (e.g., Some cats are black).
- Particular Negative (O): Some S are not P (e.g., Some cats are not black).
Understanding how these types combine is crucial for solving syllogism problems. Visual aids like Venn diagrams can also be very helpful in representing the relationships described in the statements and testing the validity of conclusions.
Important Questions from Conventional 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:
No bank is an office.
All offices are stalls.
Conclusions:
I. No bank is a stall.
II. No stall is a bank.
III. Some stalls are offices.
IV. All the stalls are offices
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 flowers are beautiful.
Vaidehi is beautiful.
Conclusions:
I. Vaidehi is a flower.
II. Some beautiful are flowers.
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 rugs are blankets.
2. All blankets are pillows.
3. Some blankets are frames.
Conclusions:
I. All pillows are rugs.
II. Some pillows are rugs.
III. All rugs are frames
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 fingers are toes.
Some toes are rings.
Some rings are hands.
Conclusions:
I. Some hands are toes.
II. Some rings are fingers.
III. Some hands are fingers.
V. Some fingers are rings.
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 polygons are angles.
All angles are diagonals.
All cones are cubes.
All cubes are decagons.
No diagonal is a cube.
Conclusions:
I. Some diagonals are polygons.
II. All diagonals are decagons.
III. No polygon is a cone.
IV. Some cubes are angles.
