In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusion(s) logically follows/follow from the statements. Statements: All cricketers are wealthy. Some wealthy are Indians. All Indians are honest. Conclusions: I. All Indians are cricketers. II. Some cricketers are honest.
Neither conclusions I nor II follows.
Understanding Syllogism Statements and Conclusions
This question involves analyzing a set of statements and determining which of the given conclusions logically follow from these statements. This type of problem is part of logical reasoning, specifically syllogisms. We must assume the statements are true, even if they contradict common knowledge, and only use the information provided in the statements to evaluate the conclusions.
Analyzing the Given Statements
Let's break down the three statements provided:
- Statement 1: All cricketers are wealthy. This is a universal affirmative statement. It means the set of cricketers is completely contained within the set of wealthy people.
- Statement 2: Some wealthy are Indians. This is a particular affirmative statement. It indicates there is an overlap between the set of wealthy people and the set of Indians. There are individuals who are both wealthy and Indian.
- Statement 3: All Indians are honest. This is a universal affirmative statement. It means the set of Indians is completely contained within the set of honest people.
Evaluating Conclusion I: All Indians are cricketers.
Conclusion I states that all Indians are cricketers. Let's see if the statements support this.
- From Statement 3, we know all Indians are honest.
- From Statement 2, we know some wealthy people are Indians.
- From Statement 1, we know all cricketers are wealthy.
Combining Statement 2 and 3 tells us that some wealthy people are honest (since some wealthy are Indians, and all Indians are honest). However, none of the statements tell us anything about the relationship between Indians and Cricketers directly. We know all Cricketers are wealthy, and some Wealthy are Indians. The group of wealthy people who are Indians might or might not include any cricketers. There is no information guaranteeing that the entire set of Indians is contained within the set of cricketers.
Using a Venn diagram approach:
- Draw a circle for 'Wealthy'. Draw a circle for 'Cricketers' completely inside the 'Wealthy' circle.
- Draw a circle for 'Indians' that overlaps with the 'Wealthy' circle (based on "Some wealthy are Indians").
- Draw a circle for 'Honest'. The 'Indians' circle must be completely inside the 'Honest' circle.
Looking at the diagram, the 'Indians' circle is not necessarily inside the 'Cricketers' circle. Therefore, the conclusion "All Indians are cricketers" does not logically follow.
Evaluating Conclusion II: Some cricketers are honest.
Conclusion II states that some cricketers are honest. Let's analyze this based on the statements.
- Statement 1: All cricketers are wealthy. (C $\rightarrow$ W)
- Statement 2: Some wealthy are Indians. (W $\cap$ I $\neq \emptyset$)
- Statement 3: All Indians are honest. (I $\rightarrow$ H)
From Statement 2 and 3, we can infer that "Some wealthy are honest" (Some W are I, and All I are H $\implies$ Some W are H). Now we need to relate this to cricketers.
We have: All C are W, and Some W are H. Can we conclude Some C are H?
Consider the structure "All A are B" and "Some B are C". This structure does not guarantee "Some A are C". For example:
- All Dogs are Animals. (A=Dogs, B=Animals)
- Some Animals are Cats. (B=Animals, C=Cats)
Does this mean "Some Dogs are Cats"? No, it does not. The overlap between Animals and Cats does not have to include the Dogs part of Animals.
Similarly, the group of wealthy people who are honest (from Statement 2 and 3) might or might not include any cricketers (who are also wealthy, from Statement 1). The statements do not provide enough information to guarantee an overlap between the 'Cricketers' set and the 'Honest' set.
Using the Venn diagram:
- The 'Cricketers' circle is inside 'Wealthy'.
- The 'Indians' circle overlaps 'Wealthy' and is inside 'Honest'.
The overlap between 'Wealthy' and 'Honest' exists where 'Indians' are. The 'Cricketers' circle is in a different part of the 'Wealthy' circle. There is no guaranteed overlap between the 'Cricketers' circle and the 'Honest' circle.
Therefore, the conclusion "Some cricketers are honest" does not logically follow.
Conclusion
Based on the logical analysis of the statements, neither Conclusion I nor Conclusion II can be definitively derived as true.
| Statement/Conclusion | Analysis | Logically Follows? |
|---|---|---|
| Statement 1: All cricketers are wealthy. | Cricketers $\subseteq$ Wealthy | Given (Assumed True) |
| Statement 2: Some wealthy are Indians. | Wealthy $\cap$ Indians $\neq \emptyset$ | Given (Assumed True) |
| Statement 3: All Indians are honest. | Indians $\subseteq$ Honest | Given (Assumed True) |
| Conclusion I: All Indians are cricketers. | Is Indians $\subseteq$ Cricketers? | No. Statements don't support this. |
| Conclusion II: Some cricketers are honest. | Is Cricketers $\cap$ Honest $\neq \emptyset$? | No. Statements don't guarantee this overlap. |
Thus, neither conclusion I nor conclusion II follows from the given statements.
Revision Table: Syllogism Rules and Types
| Type of Statement | Representation | Example |
|---|---|---|
| Universal Affirmative (A) | All S are P | All cats are mammals. |
| Universal Negative (E) | No S are P | No cats are dogs. |
| Particular Affirmative (I) | Some S are P | Some cats are black. |
| Particular Negative (O) | Some S are not P | Some cats are not friendly. |
Understanding the relationships and valid inferences between these statement types is key to solving syllogism problems. Combination rules (like A+I, A+A etc.) or Venn diagrams are common methods.
Additional Information: Solving Syllogisms with Venn Diagrams
Venn diagrams are a visual tool useful for solving syllogism problems. Each term in the statements (like Cricketers, Wealthy, Indians, Honest) is represented by a circle. The relationships described in the statements are depicted by drawing these circles and indicating overlaps or containments.
- For "All A are B", draw circle A completely inside circle B.
- For "No A are B", draw circles A and B separate from each other.
- For "Some A are B", draw circles A and B overlapping, and place an 'x' in the overlapping region to indicate that this area is not empty.
- For "Some A are not B", draw circles A and B overlapping, and place an 'x' in the part of A that does not overlap B, indicating there's something in A that is not in B.
After drawing the diagram for all statements, examine the conclusions. If the conclusion is clearly and necessarily represented in the diagram, it follows. If the diagram could be drawn in such a way that the conclusion is false while the statements are true, then the conclusion does not follow.
In this question, drawing the diagram shows no necessary overlap between Cricketers and Honest, and no containment of Indians within Cricketers, thus confirming that neither conclusion follows.
Similar Questions
Read the following statement carefully and identify the conclusion that follows.
Statement:
All games are entertainment.
All entertainment is fun.
Conclusions:
I. All games are fun
II. Some fun is entertainment.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All engineers are skilled. No unskilled person is allowed.
Conclusions:
I. All engineers are allowed.
II. No skilled person is unskilled.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All boxes are bags. Some bags are blue. No blue is a plastic.
Conclusions:
I. Some boxes are not plastic.
II. All plastics are bags.
Three statements are given, followed by four conclusions numbered I, II, III and IV. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some desks are trays.
Some trays are plates.
Some plates are desks.
Conclusions:
I. All desks are plates.
II. All plates are desks.
III. Some plates are trays.
IV. All trays are desks.
Three statements are given, followed by four conclusions numbered I, II, III and IV. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some coolers are mixers.
Some mixers are scissors.
Some scissors are knives.
Conclusions:
I. Some knives are mixers.
II. Some scissors are coolers.
III. Some knives are coolers.
IV. No knife is a mixer.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All rice are grains.
All pulses are grains.
All grains are edibles.
Conclusions:
I. All rice are edibles.
II. All pulses are edible.
III. Some edibles are grains.
In this question, three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
All balls are flowers.
All flowers are plates.
Some plates are cups.
Conclusions:
I. Some flowers are balls.
II. Some plates are flowers.
III. All cups are plates.
Three statements are given followed by three conclusions numbered I, II and Ill. Question ID: 264330143712 Status : Answered Chosen Option : 1 Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All males are boys.
Some teachers are boys.
All students are teachers.
Conclusions:
I. Some boys are males.
II. Some teachers are students.
Ill. All males are students.
Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All curtains are doormats.
Some doormats are pillows.
Some pillows are bedsheets.
Conclusions:
I. Some bedsheets are doormats.
II. Some bedsheets are curtains.
III. Some pillows are doormats.
Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some sweets are chocolates.
All chocolates are cookies.
Some cookies are healthy.
Conclusions:
I. Some sweets are cookies.
II. Some cookies are chocolates.
III. Some chocolates are sweets.
Important Questions from Conventional 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:
1. Some flowers are chemicals.
2. Some chemicals are herbs.
Conclusions:
I. No flower is a herb.
II. Some flowers are herbs.
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 students are teachers.
All teachers are professors.
Conclusions:
1. All students are professors.
2. All professors are students.
3. No teacher is a professor.
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 dentists are surgeons.
II. All the surgeons are doctors.
Conclusions:
I. Some dentists are doctors.
II. No surgeons are dentists.
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 at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
1) Some angers are griefs.
2) Some griefs are loves.
Conclusion:
I. Some griefs are angers.
II. Some loves are griefsThe 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 cows are deer.
Some deer are fishes.
Conclusion:
I. Some cows are fishes.
II. Some fishes are cows.
