The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements. Statements: 1) All butterflies are reptiles. 2) All reptiles are mammals. Conclusion: I. All mammals are butterflies.
Only conclusion II follows.
Understanding Syllogism Statements and Conclusions
This question asks us to analyze given statements and determine which of the provided conclusions logically follow. This type of problem is known as a syllogism in logical reasoning. We must strictly adhere to the information given in the statements, even if it contradicts real-world knowledge.
Analyzing the Statements
We have two statements:
- All butterflies are reptiles.
- All reptiles are mammals.
Let's represent these relationships:
- Statement 1: If something is a butterfly, then it is a reptile. (Butterflies $\rightarrow$ Reptiles)
- Statement 2: If something is a reptile, then it is a mammal. (Reptiles $\rightarrow$ Mammals)
Combining the Statements
We can combine these two statements. If all butterflies belong to the set of reptiles, and all reptiles belong to the set of mammals, then it must be true that all butterflies also belong to the set of mammals.
Think of it like sets:
- The set of Butterflies is entirely inside the set of Reptiles.
- The set of Reptiles is entirely inside the set of Mammals.
This implies that the set of Butterflies is entirely inside the set of Mammals.
So, from the statements, we can logically deduce: All butterflies are mammals.
Evaluating the Conclusions
Now let's look at the given conclusions:
Conclusion I: All mammals are butterflies.
Based on our deduction that all butterflies are mammals, does it mean all mammals are butterflies? Not necessarily. The combined statements tell us that the set of butterflies is a subset of the set of mammals. There might be many mammals that are not reptiles (and thus not butterflies). For example, based on the statements, a cow could be a mammal, but it doesn't have to be a reptile or a butterfly.
Therefore, Conclusion I does not logically follow from the given statements.
Conclusion II: All butterflies are mammals.
As we deduced from combining Statement 1 (All butterflies are reptiles) and Statement 2 (All reptiles are mammals), this conclusion logically and definitely follows.
If every single butterfly is a reptile, and every single reptile is a mammal, then it is unavoidable that every single butterfly is also a mammal.
Therefore, Conclusion II logically follows from the given statements.
Final Decision
Based on the analysis, only Conclusion II logically follows from the statements.
The correct option is the one stating that only conclusion II follows.
Revision Table: Syllogism Analysis
| Statement/Conclusion | Relationship | Logical Follows? | Explanation |
|---|---|---|---|
| Statement 1 | All Butterflies $\rightarrow$ Reptiles | Given | Accepted as true. |
| Statement 2 | All Reptiles $\rightarrow$ Mammals | Given | Accepted as true. |
| Combined Logic | All Butterflies $\rightarrow$ Mammals | Yes | Derived from Statement 1 and 2. |
| Conclusion I | All Mammals $\rightarrow$ Butterflies | No | Converse is not necessarily true. Mammals could exist that are not Butterflies. |
| Conclusion II | All Butterflies $\rightarrow$ Mammals | Yes | Directly follows from the combined logic of statements 1 and 2. |
Additional Information: Basics of Syllogisms
Syllogisms are a form of logical argument that apply deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. The structure is typically: Major Premise, Minor Premise, Conclusion.
Key principles in syllogisms like this:
- All A are B: This means the set of A is a subset of the set of B. It does NOT mean All B are A.
- Chain Rule: If All A are B, and All B are C, then it logically follows that All A are C. (This is what we saw with Butterflies, Reptiles, and Mammals).
- Assumption of Truth: In syllogism problems, you must assume the statements are true, regardless of real-world facts.
Understanding these basic rules helps in correctly determining which conclusions are logically valid deductions from the given statements.
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.
