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
Only conclusion 2 follows
Analyzing Logical Statements and Conclusions
This question asks us to evaluate conclusions based on given statements, assuming the statements are true. We need to determine which conclusions logically follow from the provided statements.
Understanding the Given Statements
Let's break down the two statements:
- Statement 1: Dhoni is a good batsman.
- Statement 2: Batsman are smart.
Statement 1 tells us something specific about Dhoni. Statement 2 tells us a general characteristic of all individuals who are batsmen – they are smart.
Examining the Conclusions
Now, let's look at the conclusions we need to evaluate:
- Conclusion 1: All smart people are batsman.
- Conclusion 2: Dhoni is smart.
Evaluating Conclusion 1: All smart people are batsman
Statement 2 says, "Batsman are smart". This means that the set of 'Batsman' is included within the set of 'Smart people'. It can be represented as: If someone is a batsman, then that person is smart.
However, this does not mean that everyone who is smart is also a batsman. There could be many smart people who are not batsmen (e.g., a smart doctor, a smart teacher, etc.).
Therefore, the statement "All smart people are batsman" cannot be definitely drawn from the given statements. It's a common logical fallacy to reverse the implication.
Let's visualize this with sets:
| Set | Relationship based on Statement 2 ("Batsman are smart") |
|---|---|
| Set of Batsman | This set is a subset of the Set of Smart People. |
| Set of Smart People | This set contains the Set of Batsman, but also potentially includes others who are smart but not batsmen. |
Based on this, Conclusion 1 does not follow.
Evaluating Conclusion 2: Dhoni is smart
We know from Statement 1 that "Dhoni is a good batsman".
We know from Statement 2 that "Batsman are smart". This means that every individual who belongs to the category of 'Batsman' also belongs to the category of 'Smart people'.
Since Dhoni belongs to the category of 'Batsman' (as stated in Statement 1), and all 'Batsman' are 'smart' (as stated in Statement 2), we can logically deduce that Dhoni is smart.
This is a valid deduction using the given statements.
Based on this, Conclusion 2 definitely follows.
Final Decision
Based on our evaluation:
- Conclusion 1: Does not follow.
- Conclusion 2: Follows.
Therefore, only Conclusion 2 can definitely be drawn from the given statements.
Revision Table: Checking Conclusions
| Conclusion | Does it Follow? | Reasoning |
|---|---|---|
| 1. All smart people are batsman. | No | Statement 2 says all batsmen are smart, not that all smart people are batsmen. This is a reversal fallacy. |
| 2. Dhoni is smart. | Yes | Dhoni is a batsman (Statement 1), and all batsmen are smart (Statement 2). Therefore, Dhoni must be smart. |
Additional Information: Understanding Deductive Reasoning
This problem is an example of deductive reasoning, specifically a type of syllogism. Deductive reasoning starts with general statements (premises) and reaches a specific, certain conclusion. If the premises are true, the conclusion must be true.
- Premise 1: All M are P (Batsmen are smart).
- Premise 2: S is M (Dhoni is a batsman).
- Conclusion: Therefore, S is P (Dhoni is smart).
This structure, known as Barbara or AAA-1 in categorical syllogisms, is a valid argument form. Our second conclusion fits this structure, confirming its validity.
Understanding the difference between "All A are B" and "All B are A" is crucial in logical reasoning problems. They are not logically equivalent.
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.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.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.
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.
