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 T is G. Some M are T. Conclusions: I. No G is T. II. All M are G.
Only conclusion I follows.
Understanding Logic Statements and Conclusions
This question asks us to analyze given statements and determine which of the provided conclusions logically follow from them. We must assume the statements are true, even if they contradict general knowledge.
Let's break down the statements and conclusions:
Analyzing the Logic Statements
We have two statements:
- Statement 1: No T is G.
- Statement 2: Some M are T.
Let's interpret these statements:
- "No T is G" means that there is absolutely no overlap between the category 'T' and the category 'G'. If something belongs to 'T', it cannot belong to 'G', and vice versa. They are mutually exclusive sets.
- "Some M are T" means that there is at least one element that belongs to both the category 'M' and the category 'T'. There is an overlap between the sets 'M' and 'T'. It does not mean *only* some M are T; it means *at least* one M is T, and there might be more, possibly even all M.
Evaluating the Conclusions
Now let's examine each conclusion based on the given statements:
- Conclusion I: No G is T.
- Conclusion II: All M are G.
Analysis of Conclusion I: No G is T
Statement 1 says "No T is G". This establishes a clear separation between the categories T and G. If nothing in T is in G, it implies the relationship works both ways: nothing in G can be in T either. If there were a G that was also a T, it would contradict Statement 1. Therefore, Conclusion I logically follows from Statement 1.
Analysis of Conclusion II: All M are G
Statement 2 says "Some M are T". This tells us there's an overlap between M and T. Statement 1 says "No T is G". This tells us T and G are separate. Let's consider the part of M that overlaps with T. Since this part is also T, and "No T is G", this overlapping part of M cannot be G. Statement 2 ("Some M are T") only guarantees that *a part* of M is T. It does not give any information about the rest of M (the part that is not T). This remaining part of M could be G, or not G, or both. We simply don't know. Furthermore, the part of M that *is* T is definitely *not* G (because "No T is G"). Therefore, we cannot conclude that "All M are G". This conclusion does not logically follow from the given statements.
Summary of Conclusions
- Conclusion I ("No G is T") follows from Statement 1 ("No T is G").
- Conclusion II ("All M are G") does not follow from the statements.
Based on this analysis, only conclusion I follows.
Revision Table: Logic Statements Summary
| Statement | Meaning | Relationship |
|---|---|---|
| No T is G | There is no element common to both T and G. | T and G are disjoint sets. |
| Some M are T | There is at least one element common to M and T. | M and T have an intersection. |
Additional Information: Understanding Logical Deduction
This type of problem is based on logical deduction, often found in topics like syllogisms. A syllogism is a form of reasoning where a conclusion is drawn from two given or assumed propositions (premises).
- Statements (Premises): These are the starting points assumed to be true.
- Conclusions: These are derived from the statements using rules of logic. A conclusion logically follows if it must be true whenever the statements are true.
- Validity: An argument is valid if the conclusion logically follows from the premises, regardless of whether the premises are actually true in the real world. In these problems, we are testing the validity of the conclusions based *only* on the provided statements.
Visual tools like Venn diagrams can often help represent these relationships and check the validity of conclusions, although the formal analysis confirms the results.
Important Questions from 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:
All dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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 follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
