Consider the given statement to be true and decide which of the given conclusion(s) logically follow(s) from the statement. Statement: Some bugs are birds. All the birds are fruits. Conclusions: 1. All the fruits are birds. 2. Some of the bugs are fruits.
Logical Reasoning Solution: Analyzing Statements and Conclusions
This question asks us to determine which of the given conclusions logically follows from the provided statements. We are given two statements and two potential conclusions. We will analyze these using logical deduction, often visualized with Venn diagrams.
Understanding the Statements
We have the following statements:
- Statement 1: Some bugs are birds.
- Statement 2: All birds are fruits.
Analyzing the Conclusions
We need to check if the following conclusions must be true based on the statements:
- Conclusion 1: All the fruits are birds.
- Conclusion 2: Some of the bugs are fruits.
Applying Logical Deduction (using Venn Diagrams)
Let's represent these statements visually using Venn diagrams:
Statement 1 says "Some bugs are birds". This means there is at least one element (bug) that is also a bird. In a Venn diagram, this is represented by overlapping circles for 'Bugs' and 'Birds', with the overlapping region being non-empty.
Statement 2 says "All birds are fruits". This means the entire set of 'Birds' is contained within the set of 'Fruits'. In a Venn diagram, the circle for 'Birds' would be drawn completely inside the circle for 'Fruits'.
Combining these, we have a situation where the 'Birds' circle is inside the 'Fruits' circle, and there is an overlap between the 'Bugs' circle and the 'Birds' circle. Since the 'Birds' circle is inside the 'Fruits' circle, the area where 'Bugs' and 'Birds' overlap must also be an area where 'Bugs' and 'Fruits' overlap.
Evaluating Conclusion 1: All fruits are birds.
Look at our combined representation. Does the statement "All fruits are birds" necessarily follow? No. While all birds are fruits, the set of fruits can be much larger than the set of birds. There can be fruits that are not birds (and according to the diagram, there must be, unless the sets of Birds and Fruits are identical, which is not implied by "All birds are fruits"). Therefore, Conclusion 1 does not logically follow from the statements.
Evaluating Conclusion 2: Some of the bugs are fruits.
From Statement 1, we know "Some bugs are birds". This means there is a non-empty group of items that are both bugs and birds. From Statement 2, we know "All birds are fruits". This means that every item in the 'Birds' set is also in the 'Fruits' set.
Since there are some bugs that are birds, and all birds are fruits, it logically follows that those specific bugs (the ones that are birds) must also be fruits. Therefore, there must be some bugs that are fruits. Conclusion 2 logically follows from the statements.
Summary of Analysis
- Conclusion 1 (All fruits are birds) does not follow.
- Conclusion 2 (Some bugs are fruits) follows.
Based on this analysis, only Conclusion 2 follows from the given statements.
Revision Table: Checking Statement Types and Inference
| Statement/Conclusion | Type | Logical Form |
|---|---|---|
| Statement 1: Some bugs are birds. | Particular Affirmative (I) | Some S are P |
| Statement 2: All birds are fruits. | Universal Affirmative (A) | All P are Q |
| Conclusion 1: All fruits are birds. | Universal Affirmative (A) | All Q are P |
| Conclusion 2: Some of the bugs are fruits. | Particular Affirmative (I) | Some S are Q |
The combination of an I statement ("Some S are P") and an A statement ("All P are Q") can validly yield an I conclusion ("Some S are Q"). This is a standard form of a syllogism (specifically, IAI-3 or IAI-4, depending on the arrangement, but the core inference holds).
Additional Information: Categorical Propositions
Statements in this type of logical reasoning are often classified as categorical propositions. There are four main types:
- Universal Affirmative (A): All S are P (e.g., All birds are fruits).
- Universal Negative (E): No S are P (e.g., No bugs are birds).
- Particular Affirmative (I): Some S are P (e.g., Some bugs are birds).
- Particular Negative (O): Some S are not P (e.g., Some bugs are not birds).
Understanding these types helps in analyzing the relationships between categories (like bugs, birds, and fruits) and determining valid inferences.
Similar Questions
Consider the given statements true and decide which of the given conclusion(s) logically follow(s) from the statements.
Statements:
1. All reds are yellows.
2. Some yellow are not greens.
Conclusions:
1. Some yellow are reds
2. All yellow are greens
Consider the given statements to be true and decide which of the conclusions logically follow(s) from the given statements.
Statement:
All fruits are trees. Some trees are birds.
Conclusions:
1. Some birds are trees.
2. Some trees are fruits.
Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some cars are bikes.
All bikes are trucks.
Conclusions:
(I) Some trucks are cars.
(II) All trucks are cars.Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some gold are silver.
Some silver are diamonds.
Conclusions:
(I) Some diamonds are gold.
(II) Some silver are gold.Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some bulbs are sands.
All bulbs are candles.
Conclusion:
(I) Some candles are bulbs.
(II) No candle is a sand.
Consider the given statement to be true and decide which of the conclusions logically follows (s) from the statements.
Statements:
Some angels are gods.
All living being are gods.
Conclusions:
1. Some gods are angels.
2. Some living beings are gods.Consider the given statement as true and decide which of the given conclusions can definitely be drawn from the given statements.
Statements:
Dhoni is a good batsman.
Batsman are smart.
Conclusions:
1. All smart people are batsman
2. Dhoni is smart.Given below are two statement, followed by two conclusion, I and II. You have to consider the statement to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow(s) from the given statements.
Statement 1: No quadrilaterals are polygons.
Statement 2: All polygons are rhombuses.
Conclusion I: Some rhombuses are quadrilaterals.
Conclusion II: Some rhombuses are polygons.Consider the given statement to be true and decide which of the given conclusions can definitely be drawn from the given statements.
Statements:
Some lawyers are females. Some females are mothers.
Conclusion:
1. Some mothers are females.
2. Some lawyers are mothers.Consider the given statements to be true and decide which of the given conclusions can definitely be drawn from the statements.
Statements:
All sharks are fish. No fish is a snake.
Conclusions:
1. No snake is a shark.
2. No shark is a snake.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. 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:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled 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:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. 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:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
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:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
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:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
