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: I. All M are Q. II. No L is Q. Conclusions: I. No M is L. II. Some L are not M.
Both conclusions I and II follow
Logical Reasoning: Syllogism Solution Explained
This question asks us to analyze two statements and determine which of the given conclusions logically follow from them, assuming the statements are true.
Analyzing the Statements
- Statement I: All M are Q.
- Statement II: No L is Q.
Let's break down what these statements mean. Statement I tells us that the entire group or set M is contained within the group or set Q. Think of it like this: if something is an M, it must also be a Q.
Statement II tells us that there is absolutely no overlap between the group or set L and the group or set Q. If something is an L, it cannot be a Q, and vice versa.
Evaluating the Conclusions Based on Statements
We can visualize this relationship using a conceptual Venn Diagram. Imagine three circles representing sets M, Q, and L.
- Statement I means the M circle is completely inside the Q circle.
- Statement II means the L circle is completely outside the Q circle.
Now, let's look at the conclusions:
Conclusion I: No M is L.
Based on our understanding from the statements:
- All M are inside Q.
- No L is inside Q (L is outside Q).
If L is completely outside Q, and M is completely inside Q, then there is no way for L and M to overlap. Therefore, it logically follows that No M is L. This conclusion is true.
Conclusion II: Some L are not M.
Again, consider the relationship derived from the statements:
- No L is Q.
- All M are Q.
Since No L is Q, it means every single element of L is outside of Q. And because All M are Q, it means M is inside Q. If every L is outside Q, and M is inside Q, then every L must necessarily be outside M. In other words, No L is M.
If No L is M is true (meaning not a single L is an M), then it is certainly true that Some L are not M. If *all* Ls are not Ms, then *some* Ls are definitely not Ms. This conclusion also logically follows.
Summary of Conclusions
From the statements "All M are Q" and "No L is Q", we deduced that:
- Conclusion I: No M is L - This follows.
- Conclusion II: Some L are not M - This follows.
Both conclusions are logically supported by the given statements.
Revision Table: Syllogism Rules
| Statement Type | Relation | Example Structure |
|---|---|---|
| Universal Affirmative (A) | All X are Y | X $\subseteq$ Y |
| Universal Negative (E) | No X is Y | X $\cap$ Y = $\emptyset$ |
| Particular Affirmative (I) | Some X are Y | X $\cap$ Y $\neq$ $\emptyset$ |
| Particular Negative (O) | Some X are not Y | Some X $\notin$ Y |
Additional Information: Understanding Syllogisms
Syllogisms are a form of logical reasoning where a conclusion is drawn from two or more premises (statements). The statements provide information about the relationships between different categories or terms. The goal is to determine if a conclusion necessarily follows from these relationships, assuming the statements are true, even if they contradict general knowledge.
Key points to remember when solving syllogism problems:
- Always assume the statements are true.
- Do not use any outside knowledge.
- Use methods like Venn Diagrams or rules of logic to check the validity of the conclusions.
- A conclusion follows only if it is impossible for it to be false when the statements are true.
In this specific problem, the combination of "All M are Q" and "No L is Q" creates a clear separation between M and L, making both "No M is L" and consequently "Some L are not M" valid conclusions.
Important Questions from Conventional Syllogism
In this question, three statements followed by two conclusions numbered I and II have been given. You have to take the given statements to be true even if they seem to be at variance from the commonly facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some flats are apartments.
No apartment is a hall.
Some halls are rooms.
Conclusions: I. At least some rooms are flats.
II. No apartment is a room.
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:
I. Some blue are red.
II. Some green are red.
Conclusions:
I. No blue is green.
II. No red is green.
Given below are two statements, Consider these statements to be true even if they seem factuality absurd, Read the conclusions and then decide which of the given conclusions logically follow(s) from the given statements?
Statements :
1. All vases are flowers.
2. No flowers is a plant.
Conclusions :
1. No vases is a plant.
2. Some plant are vases
In the question two statements are given, followed by three conclusions, I, II and III. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement 1 : Some cars are scooters.
Statement 2 : All scooters are buses.
Conclusion I : Some scooters are cars.
Conclusion II : Some buses are cars.
Conclusion III : All cars are buses.
In the question below are given three statements followed by two conclusions. You have to take each of the given statements to be true. Read the conclusions and then decide which of the conclusions can be logically derived.
Statements:
Some schools are colleges.
No college is university.
All universities are hospitals.
Conclusions:
I. Some schools are universities.
II. At least some hospitals are colleges.
