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 conclusions logically follows/follow from the statements.
Statements:
I. No picture is an album.
II. All albums are frames.
III. Some frames are portraits.
Conclusions:
I. No picture is a frame.
II. Some pictures are portraits.
Syllogism Reasoning: Statements and Conclusions Analysis
This problem involves logical reasoning, specifically a type of syllogism. We need to determine which of the given conclusions can be logically derived from the provided statements. We must assume the statements are true, even if they seem unusual.
Understanding the Statements
Let's break down the information given:
- Statement I: No picture is an album. This means the set of 'pictures' and the set of 'albums' are completely separate. If something is a picture, it cannot be an album, and vice versa.
- Statement II: All albums are frames. This means the entire set of 'albums' is contained within the larger set of 'frames'. If something is an album, it must also be a frame.
- Statement III: Some frames are portraits. This indicates there is an overlap between the set of 'frames' and the set of 'portraits'. At least one frame is a portrait.
Analyzing the Conclusions
Now, let's examine each conclusion based on the statements:
Analysis of Conclusion I: No picture is a frame.
- From Statement I, we know 'pictures' and 'albums' are separate.
- From Statement II, we know 'albums' are a subset of 'frames'.
- Statement III tells us 'frames' and 'portraits' overlap.
- Consider the relationship between 'pictures' and 'frames'. Since all albums are frames (Statement II), and no picture is an album (Statement I), it means pictures are outside the album category, but albums are *inside* the frame category. This doesn't prevent pictures from being *other types* of frames that are not albums. For example, a photo print could be considered a 'picture' and also a type of 'frame' (like a framed photograph), without being an 'album' (like a photo album book).
- Therefore, we cannot definitively conclude that no picture is a frame. It's possible for a picture to be a frame.
Conclusion I does not logically follow.
Analysis of Conclusion II: Some pictures are portraits.
- We know from Statement III that there is an overlap between 'frames' and 'portraits'.
- We know 'pictures' are separate from 'albums' (Statement I), and 'albums' are within 'frames' (Statement II).
- The statements establish connections: Pictures (P), Albums (A), Frames (F), Portraits (P'). Relationships: P is disjoint from A; A is a subset of F; F overlaps with P'.
- There is no direct or indirect link established between the set of 'pictures' and the set of 'portraits'. The overlap between frames and portraits might occur in a part of the 'frames' set that has no intersection with the 'pictures' set.
- For instance, imagine frames containing only paintings (which are portraits) and frames containing only photos (which are pictures). These could be separate categories within the broader 'frames' set.
- Therefore, we cannot conclude that some pictures are portraits based solely on the given statements.
Conclusion II does not logically follow.
Final Determination
Based on the analysis, neither Conclusion I nor Conclusion II can be logically derived from the given statements. The relationships between the sets (pictures, albums, frames, portraits) do not guarantee these conclusions.
Similar Questions
- 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 conclusions logically follows/follow from the statements.
Statements:
I. Some tables are chairs.
II. All desks are chairs.
III. No chair is a fan.
Conclusions:
I. Some desks are tables.
II. Some fans are desks. - 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 conclusions logically follows/follow from the statements.
Statements:
I. All tables are charts.
II. Some charts are graphs.
III. Some graphs are pies.
Conclusions:
I. No table is a graph.
II. Some pies are charts. - 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 conclusions logically follows/follow from the statements.
Statements:
All boxes are squares.
All squares are rectangles.
All rectangles are figures.
Conclusions:
I. All boxes are figures.
II. All squares are figures. 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 given conclusions logically follow(s) from the statements.
Statements:
Some fractions are marts.
No mart is a stud.
All studs are frogs.
Conclusions:
I. Some fractions are definitely not studs.
II. Some fractions are definitely not marts.
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:
Some calculators are lanterns.
Some lanterns are mobiles.
Conclusions:
I. All mobiles are calculators.
II. No mobile is a lantern.
III. Some mobiles are lanterns.
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 parrots are crows.
All crows are eagles.
Conclusions:
I. All parrots are eagles.
Il. Some crows are parrots.
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 from the statements.
Statements:
No certificate is a paper.
All pens are papers.
Conclusions:
I. No certificate is a pen.
II. No paper is a certificate.
III. Some papers are pens.
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:
Some officers are clerks.
All clerks are workers.
Conclusions:
I. Some workers are officers.
Il. No worker is an officer.
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 chargers are phones.
No phone is a watch.
Conclusions:
I. All phones are chargers.
Il. No charger is a watch.
Ill. No watch is a phone.
Two 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 wallets are bags.
Some bags are envelopes.
Conclusions:
I. Some wallets are envelopes.
II. No wallet is an envelope.
III. No bag is an envelope.
Important Questions from 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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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:
Some actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
