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
Only conclusion 1 follows.
Statements Analysis for Logical Reasoning
This question is based on the topic of logical syllogism, where we need to determine which conclusions logically follow from a set of given statements. We will analyze each statement and conclusion using logical deduction, which can be visualized using Venn diagrams.
Statements Breakdown: Vases and Flowers
Let's break down the two statements provided:
- Statement 1: All vases are flowers.
This statement tells us that the entire set of 'vases' is completely included within the set of 'flowers'. In simpler terms, every single vase is also a flower. There are no vases that are not flowers.
Mathematically, we can represent this as: $\text{Vases} \subseteq \text{Flowers}$
- Statement 2: No flowers is a plant.
This statement indicates that there is absolutely no overlap between the set of 'flowers' and the set of 'plants'. They are two completely separate and distinct categories. If something is a flower, it cannot be a plant, and vice-versa.
Mathematically, we can represent this as: $\text{Flowers} \cap \text{Plants} = \emptyset$
Conclusions Evaluation: Plant and Vases
Now, let's examine each conclusion based on the truth of the given statements.
Conclusion 1: Vases and Plant Relationship
- From Statement 1, we know that all 'vases' are part of the 'flowers' group.
- From Statement 2, we know that the 'flowers' group has no members in common with the 'plants' group.
- If all vases are flowers, and no flowers are plants, then it logically follows that no vases can be plants. The set of vases is a subset of flowers, and if flowers don't intersect with plants, then its subset (vases) also cannot intersect with plants.
- Therefore, this conclusion logically follows from the given statements.
- Venn Diagram thought process: Imagine a circle for 'Vases' entirely inside a larger circle for 'Flowers'. Now imagine a third circle for 'Plants' that does not touch the 'Flowers' circle at all. Since 'Vases' is inside 'Flowers', the 'Vases' circle also cannot touch the 'Plants' circle.
- Mathematical representation:
Given: $\text{Vases} \subseteq \text{Flowers}$
Given: $\text{Flowers} \cap \text{Plants} = \emptyset$
From these, it implies: $\text{Vases} \cap \text{Plants} = \emptyset$ (No vases are plants).
Conclusion 2: Plant and Vases Overlap
- We have already established from Conclusion 1's analysis that "No vases is a plant" logically follows. This means that the set of 'vases' and the set of 'plants' have no common elements.
- If no vases are plants, then it is impossible for "Some plant are vases" to be true. These two statements are contradictory.
- Therefore, this conclusion does not logically follow from the given statements. In fact, it is false based on the given statements.
Conclusions Summary Table
Here's a quick summary of our findings:
| Conclusion | Logically Follows? | Reasoning |
|---|---|---|
| No vases is a plant. | Yes | Since all vases are flowers, and no flowers are plants, then no vases can be plants. |
| Some plant are vases. | No | This contradicts the direct implication that no vases are plants. |
Final Logical Decision
Based on our analysis, only Conclusion 1 logically follows from the given statements.
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.
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. All A are S.
II. No D is A.
Conclusions:
I. Some S are A.
II. All S are D.
III. No A is D.
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. Some land are hard.
II. No stone is land.
Conclusions:
I. Some hard are land.
II. Some stone are hard.
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.
