Statements:
1. Some Books are Pencils.
2. All Pencils are Sharpeners.
3. All Books are Bags.
Conclusions:
I. Some Bags are Sharpeners.
II. Some Sharpeners are Books.
III. Some Sharpeners are Pencils.
Analyzing Statements and Conclusions in Logical Reasoning
This question requires us to analyze a set of statements and determine which of the given conclusions logically follow from them. We need to assume the statements are true, even if they seem unusual, and apply logical deduction.
Given Statements
- 1. Some Books are Pencils.
- 2. All Pencils are Sharpeners.
- 3. All Books are Bags.
Given Conclusions
- I. Some Bags are Sharpeners.
- II. Some Sharpeners are Books.
- III. Some Sharpeners are Pencils.
Logical Analysis of Statements
Let's break down the relationships:
- Statement 1 (Some Books are Pencils) tells us there's an overlap between the category 'Books' and 'Pencils'. This means at least one book is a pencil, and possibly more.
- Statement 2 (All Pencils are Sharpeners) means the entire category of 'Pencils' is contained within the category 'Sharpeners'.
- Statement 3 (All Books are Bags) means the entire category of 'Books' is contained within the category 'Bags'.
We can visualize this using Venn diagrams or by combining the statements:
- From Statement 1 and 2: Since some Books are Pencils, and all Pencils are Sharpeners, it logically follows that those specific Books which are Pencils must also be Sharpeners. Therefore, Some Books are Sharpeners.
- From Statement 3: All Books are Bags. This means the category 'Books' is a subset of the category 'Bags'.
Evaluating Each Conclusion
Conclusion I: Some Bags are Sharpeners
From our analysis above, we deduced that "Some Books are Sharpeners". We also know from Statement 3 that "All Books are Bags". If a particular item is both a Book and a Sharpener, and all Books are also Bags, then that item must be a Bag and a Sharpener. Therefore, Some Bags are Sharpeners. This conclusion logically follows.
Conclusion II: Some Sharpeners are Books
We established from Statements 1 and 2 that "Some Books are Sharpeners". The relationship "Some A are B" is symmetrical, meaning it also implies "Some B are A". Therefore, if Some Books are Sharpeners, it directly implies that Some Sharpeners are Books. This conclusion logically follows.
Conclusion III: Some Sharpeners are Pencils
Statement 2 explicitly states "All Pencils are Sharpeners". Statement 1 ("Some Books are Pencils") implies that Pencils exist. Since all Pencils are Sharpeners, and Pencils exist, it must be true that Some Sharpeners are Pencils (specifically, those Sharpeners that are Pencils). This conclusion logically follows.
Final Decision
Based on the logical analysis:
- Conclusion I follows.
- Conclusion II follows.
- Conclusion III follows.
Therefore, all three conclusions logically follow from the given statements.
Similar Questions
Two 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 follow(s) from the statements.
Statements:
No book is a novel.
All novels are diaries.
Conclusions:
I. All diaries can never be books.
II. Some books are diaries.
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 rhombuses are tangents.
All chords are tangents.
Conclusions:
I. Some rhombuses being chords is a possibility.
II. Some tangents are rhombuses.
Three statements are followed by three conclusions numbered I, II, III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follows from the given statements.
Statements :
No Mango is a banana.
No banana is a guava.
Some guavas are oranges.
Conclusions :
(I) Some mangoes are oranges.
(II) Some guavas are mangoes.
(III) No orange is a banana.
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 tigers are fishes.
No elephant is a tiger.
Some deer are tigers.
Conclusions:
I. Some fishes are deer.
II. No elephant is a deer.
III. No deer is a fish.
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.
Statement :
All Bananas are Grapes.
All Papayas are Pineapple.
Some Pineapples are Banana.
Conclusions:
(I) Some Papayas are Grapes.
(II) Some Grapes are Pineapples.
(III) Some Bananas are Papayas.
Two 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 follow(s) from the statements.
Statements:
Some defects are problems.
Some problems are solutions.
Conclusions:
I. Some defects being solutions is a possibility.
II. No solution is a defect.
Given below are two statements and two conclusions. Take the statements to be true even if they are at variance with commonly known facts, and decide whether the conclusion(s) follow(s) the given statements.
Statements:
Some bags are sacks.
Some sacks are juts.
Conclusions:
I. Some bags are juts.
II. Some juts are sacks.
Two statements are given, followed by two conclusions numbered I and II. Taking the statements to be true, even if they seem to be at variance from commonly known facts, decide which of the conclusions logically follows from the statements.
Statements:
All cycles are buses.
Some buses are trains.
Conclusions:
I. No cycle is train.
II. All cycles are trains.
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.
Statement:
Some figs are orange.
All oranges are grapes.
All mangoes are oranges.
Conclusions:
(I) Some figs are grapes.
(II) All mangoes are grapes.
(III) Some mangoes are figs.
Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at have to consider these 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 given statements.
Statements:
No bench is a table.
No board is a bench.
Some benches are chalks.
Conclusions:
(I) Some chalks are benches.
(II) Some chalks are not tables.
(III) Some chalks are not boards.
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.
