In the following questions, two statements S1 & S2 are given followed by two conclusions I & II. Taking the two statements S1 and S2 as true, decide which one of the answer (A), (B), (C), (D) logically follows.
Statements : S1 : Some players are brave. S2 : All boys are brave. Conclusions : I : Some players are boys. II : Some boys are players.
Neither I nor II follows.
To determine which conclusion logically follows from the given statements, we need to analyze each statement and conclusion carefully. We will use the principles of logical deduction, often visualized with Venn diagrams, to assess the validity of the conclusions. Understanding the relationship between the sets defined by the statements is key to solving these logical reasoning problems.
Statements Analysis
Let's first understand the two given statements. In these types of logical reasoning problems, it's helpful to define the sets involved:
| Set Symbol | Description |
|---|---|
| P | Players |
| B | Brave individuals |
| O | Boys |
- Statement S1: Some players are brave. This statement implies that there is at least one player who is also brave. It suggests an overlap or intersection between the set of 'players' and the set of 'brave' individuals. In terms of sets, this means the intersection of P and B is not empty: $P \cap B \neq \emptyset$.
- Statement S2: All boys are brave. This statement implies that the entire set of 'boys' is included within the set of 'brave' individuals. There are no boys who are not brave. In terms of sets, this means O is a subset of B: $O \subseteq B$.
Conclusions Evaluation
Now, let's evaluate each conclusion based on the combined information from S1 and S2. A conclusion logically follows only if it is necessarily true given the truth of the statements.
Conclusion I Evaluation: Some Players are Boys
- Conclusion I: Some players are boys. This means there is at least one player who is also a boy. In set notation, this implies the intersection of P and O is not empty: $P \cap O \neq \emptyset$.
- From Statement S1, we know that some players are brave ($P \cap B \neq \emptyset$).
- From Statement S2, we know that all boys are brave ($O \subseteq B$).
- Consider a scenario where both statements are true, but Conclusion I is false. Imagine the set of 'Brave' people as a large group. Inside this group, we have all 'Boys'. The set of 'Players' overlaps with the 'Brave' set. However, this overlap could happen entirely within the part of 'Brave' that is outside the 'Boys' set. For example, if 'Brave' people are those who like chocolate, 'Players' are those who play cricket, and 'Boys' are those who study in school.
- S1: Some cricket players (players) like chocolate (brave). This is possible.
- S2: All school students (boys) like chocolate (brave). This is also possible.
- Does it logically follow that some cricket players (players) are school students (boys)? Not necessarily. A cricket player who likes chocolate might not be a school student, and a school student who likes chocolate might not play cricket. There is no information in the statements that forces an overlap between the set of players and the set of boys.
- Therefore, Conclusion I does not logically follow.
Conclusion II Evaluation: Some Boys are Players
- Conclusion II: Some boys are players. This means there is at least one boy who is also a player. In set notation, this implies the intersection of O and P is not empty: $O \cap P \neq \emptyset$.
- This conclusion is essentially asking the same thing as Conclusion I, just stated in the reverse order (due to the commutative property of intersection, $A \cap B$ is the same as $B \cap A$). If 'some players are boys' is not necessarily true, then 'some boys are players' is also not necessarily true.
- The same counter-example and reasoning used for Conclusion I applies here. The statements do not provide sufficient information to establish a definite overlap between the set of 'boys' and the set of 'players'. The overlap of 'Players' with 'Brave' could occur in a segment of 'Brave' that has no intersection with 'Boys'.
- Therefore, Conclusion II does not logically follow.
Deduction Summary
Based on our detailed analysis, neither Conclusion I nor Conclusion II can be logically derived from the given statements. While it is possible for some players to be boys, or some boys to be players in a real-world scenario, the statements provided do not guarantee this relationship. In logical reasoning, a conclusion must necessarily follow from the premises for it to be considered valid.
Thus, the correct option is that neither Conclusion I nor Conclusion II follows.
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.
