In the following question below are given some statements followed by some conclusions based on those statements. 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. No F is N. II. All N are L. Conclusions: I. All F are L. II. All N are F. III. Some L are N.
Only conclusion III follows
Understanding Syllogism Statements and Conclusions
This question deals with syllogism, a type of logical argument where conclusions are drawn from two or more given statements. We need to analyze the relationship between different categories based on the provided statements and determine which conclusions logically follow.
Analyzing the Syllogism Statements
We are given two statements:
- Statement I: No F is N.
- Statement II: All N are L.
Let's break down what these statements mean:
- "No F is N" means there is no overlap between the category F and the category N. They are mutually exclusive.
- "All N are L" means that the category N is completely included within the category L. Every member of N is also a member of L.
Visualizing with Venn Diagrams
We can represent these statements using Venn diagrams to better understand the relationships:
- For Statement I (No F is N): Draw two separate circles, one for F and one for N, with no overlapping area.
- For Statement II (All N are L): Draw a circle for N completely inside a larger circle for L.
Now, let's combine these. The circle for N is inside the circle for L, and the circle for F is separate from the circle for N. The position of the F circle relative to the L circle is not fully determined by the statements. F could be entirely outside L, partly inside L, or entirely inside L, as long as it does not overlap with the N part of L.
Evaluating the Syllogism Conclusions
Based on the statements and our understanding, let's evaluate each conclusion:
- Conclusion I: All F are L.
Our combined diagram shows that the F circle is separate from the N circle (which is inside L). However, there's nothing in the statements that requires F to be inside L. F could be outside L entirely or overlap with L. Since it's not necessarily true in all possible scenarios allowed by the statements, this conclusion does not logically follow.
- Conclusion II: All N are F.
Statement I explicitly says "No F is N". If "No F is N", then it directly implies "No N is F". Therefore, it is impossible for "All N to be F". This conclusion contradicts the given statements and thus does not follow.
- Conclusion III: Some L are N.
Statement II says "All N are L". If all members of category N are also members of category L, then the category N is a part of the category L. As long as there are members in N (syllogism assumes existence for standard interpretation), these members are also in L. Therefore, some part of L consists of N. This conclusion logically follows from Statement II.
Summary of Syllogism Conclusions
Based on our analysis:
- Conclusion I: All F are L. Does Not Follow.
- Conclusion II: All N are F. Does Not Follow.
- Conclusion III: Some L are N. Logically Follows.
Therefore, only conclusion III follows from the given statements.
| Statement | Interpretation |
|---|---|
| No F is N. | F and N are separate groups. |
| All N are L. | The entire group N is inside the group L. |
| Conclusion | Logical Deduction | Follows? |
|---|---|---|
| All F are L. | Not guaranteed by statements. F can be outside or partially in L. | No |
| All N are F. | Contradicts "No F is N". | No |
| Some L are N. | If all N are L, then the N group is part of L, meaning some part of L is N. | Yes |
Revision Table: Key Syllogism Concepts
| Concept | Description |
|---|---|
| Statements | The initial premises or propositions given in a syllogism. |
| Conclusions | Deductions drawn logically from the given statements. |
| Logically Follows | A conclusion that is true whenever the given statements are true. |
| Venn Diagrams | Visual tool to represent the relationship between categories in syllogism statements. |
Additional Information on Syllogism
Syllogism problems test your ability to derive conclusions based purely on the information provided in the statements, without using outside knowledge. The statements might seem counter-intuitive, but for the purpose of the problem, they must be taken as absolutely true.
Standard categorical statements in syllogism include:
- All A are B (Universal Affirmative)
- No A is B (Universal Negative)
- Some A are B (Particular Affirmative)
- Some A are not B (Particular Negative)
Understanding how these statement types relate to each other (e.g., "All N are L" implies "Some L are N") is crucial for solving syllogism questions accurately.
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.
