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 blankets are quilts. Some quilts are bedsheets. Conclusions: I. All quilts are blankets. II. All blankets are bedsheets.
Neither conclusion I nor II follows
Syllogism Statements and Conclusions Analysis
This question asks us to analyze two statements and determine which of the given conclusions logically follow from them. This type of problem is known as syllogism, a common topic in logical reasoning tests.
Understanding the Statements
We are given the following statements:
- Some blankets are quilts.
- Some quilts are bedsheets.
We must assume these statements are true, even if they contradict general knowledge. We need to derive conclusions based only on the information provided in these statements.
Analyzing the Conclusions
Now let's examine each conclusion based on the given statements.
Conclusion I: All quilts are blankets.
The first statement says, "Some blankets are quilts." This indicates that there is at least one blanket that is also a quilt, and at least one quilt that is also a blanket. However, it does not provide any information about all quilts. It's possible that some quilts are blankets, but others are not. The statement "Some A are B" does not imply "All B are A".
For example, if we say "Some students are smart", it doesn't mean "All smart people are students". Similarly, "Some blankets are quilts" does not mean "All quilts are blankets".
Therefore, Conclusion I does not logically follow from the statements.
Conclusion II: All blankets are bedsheets.
The statements connect blankets to quilts (Some blankets are quilts) and quilts to bedsheets (Some quilts are bedsheets). Both are "some" relationships. When you have two statements like "Some A are B" and "Some B are C", you cannot draw a definite universal conclusion (like "All A are C" or "All C are A") or even a definite particular conclusion (like "Some A are C" or "Some A are not C" in all cases).
Let's consider possible scenarios (represented conceptually like Venn diagrams):
- Scenario 1: Some blankets are quilts, and those particular quilts are also some bedsheets. In this case, some blankets might be bedsheets.
- Scenario 2: Some blankets are quilts, and a completely different set of quilts (not including the ones that are blankets) are bedsheets. In this case, blankets and bedsheets might have no overlap at all.
Since we cannot definitively say that all blankets are bedsheets in all possible interpretations of the statements, Conclusion II does not logically follow.
Summary of Analysis
| Conclusion | Based on Statements | Logically Follows? | Reason |
|---|---|---|---|
| I. All quilts are blankets. | Some blankets are quilts. | No | "Some A are B" does not imply "All B are A". |
| II. All blankets are bedsheets. | Some blankets are quilts. Some quilts are bedsheets. |
No | Two "Some" statements connecting terms do not guarantee a universal relationship between the extreme terms (blankets and bedsheets). |
Based on the analysis, neither Conclusion I nor Conclusion II can be logically deduced from the given statements.
Conclusion
Therefore, neither conclusion I nor conclusion II follows from the given statements.
Revision Table: Syllogism Basics
| Statement Type | Relationship | Example |
|---|---|---|
| Universal Affirmative (A) | All A are B | All dogs are mammals. |
| Universal Negative (E) | No A are B | No cats are dogs. |
| Particular Affirmative (I) | Some A are B | Some students are smart. |
| Particular Negative (O) | Some A are not B | Some students are not smart. |
Additional Information: Syllogism Rules and Venn Diagrams
Syllogism problems involve deductive reasoning. We use the given statements (premises) to infer conclusions. A conclusion is valid only if it *must* be true whenever the premises are true. If there is even one possibility where the premises are true but the conclusion is false, the conclusion is not valid.
Venn diagrams are often helpful tools for visualizing syllogisms. Each set (like 'blankets', 'quilts', 'bedsheets') can be represented by a circle. Overlapping circles show a 'some' relationship, and separate circles show a 'no' relationship. For universal statements ('all' or 'no'), entire circles or non-overlapping parts are shaded or marked.
For the statements:
- Some blankets are quilts: Draw two overlapping circles for Blankets and Quilts. Mark the overlapping region to show it's not empty.
- Some quilts are bedsheets: Draw a third circle for Bedsheets. This circle overlaps with the Quilts circle. Mark the overlapping region between Quilts and Bedsheets.
When checking conclusions:
- Conclusion I (All quilts are blankets): Look at the Quilts circle. Is the entire Quilts circle inside the Blankets circle based on the markings? No, only the overlapping part is confirmed to be Blankets.
- Conclusion II (All blankets are bedsheets): Look at the Blankets circle and the Bedsheets circle. Is the entire Blankets circle inside the Bedsheets circle? The statements only link Blankets to Quilts, and Quilts to Bedsheets via 'some' relationships. There is no guaranteed overlap covering all blankets.
Using Venn diagrams confirms that neither conclusion necessarily follows.
Similar Questions
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 curtains are pillows.
No pillow is a bedsheet.
Some curtains are bedsheets.
Conclusions:
I. No curtain is a bedsheet.
II. No pillow is a curtain.
III. Some bedsheets are curtains.
IV. Some pillows are curtains.
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 dates are cashews.
All cashews are raisins.
Some raisins are almonds.
Conclusions:
I. All almonds being dates is a possibility.
II. All dates are raisins.
III. No cashew is an almond.
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 vehicles are helicopters.
All helicopters are cars.
Conclusions:
I. All vehicles are cars.
II. Some vehicles are cars.
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 plants are flowers.
Some flowers are fruits.
All flowers are gardens.
Conclusions:
I. Some gardens are plants.
II. Some fruits are gardens.
III. Some gardens are flowers.
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 teachers are engineers.
All clerks are teachers.
Conclusions:
I. Some engineers are clerks.
II. Some teachers are clerks.
III. Some clerks are not engineers.
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 classrooms are schools.
No school is a park.
All houses are parks.
Conclusions:
I. No house is a classroom.
II. No park is a classroom.
III. No school is a house.
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 fans are hammers.
All hammers are fishes.
Conclusions:
I. No fans are fishes.
II. Some fans are fishes.
Read the given statements and conclusions carefully. Assuming that the information given in the statement 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 fans are coolers.
All coolers are equipment.
Some equipment are mobiles.
Conclusions:
I. Some equipments are fans.
II. Some mobiles are fans.
III. No equipment is fan and cooler both
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 inkpots are kettles.
All utensils are candies.
No kettle is utensil.
Conclusions:
1. Some inkpots are candies.
2. Some kettles are inkpots.
3. Some candies are inkpots.
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 holders are hangers.
All hangers are hammers.
Some hammers are axes.
Conclusions:
I. Some axes are hangers.
II. Some hammers are holders.
III. Some hangers are holders.
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.
