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.
Only conclusions I and II follow
Logical Reasoning: Syllogism Analysis of Statements and Conclusions
This question requires us to analyze the given statements based on principles of logical reasoning, specifically syllogisms, and determine which of the conclusions logically follow from these statements.
Understanding the Syllogism Statements
We are given three statements:
- Statement 1: All dates are cashews.
- Statement 2: All cashews are raisins.
- Statement 3: Some raisins are almonds.
In syllogism, "All A are B" means that the set of A is completely contained within the set of B. "Some A are B" means there is at least one element common to both sets A and B.
Analyzing the Statements and Their Combinations
Let's break down the statements:
- "All dates are cashews" can be represented as Date → Cashew. This means the set of Dates is a subset of the set of Cashews.
- "All cashews are raisins" can be represented as Cashew → Raisin. This means the set of Cashews is a subset of the set of Raisins.
- Combining Statement 1 and Statement 2: Since all dates are cashews and all cashews are raisins, it logically follows that all dates must also be raisins. Date → Cashew → Raisin.
- "Some raisins are almonds" can be represented as Raisin ∩ Almond is not an empty set. This means there is an intersection between the set of Raisins and the set of Almonds. However, this statement does not give us any definite information about the relationship between Almonds and the subsets of Raisins (like Cashews or Dates).
Evaluating the Conclusions
Now, let's examine each conclusion based on our analysis of the statements.
Conclusion I: All almonds being dates is a possibility.
We know that Some Raisins are Almonds. We also know that All Dates are Raisins. The set of Dates is a part of the set of Raisins. Since some portion of Raisins is Almonds, it is possible that the portion of Raisins that are also Dates might overlap with the portion of Raisins that are Almonds. There is no information in the statements that prevents this overlap from including all Almonds within the Dates subset of Raisins. Therefore, it is possible for all almonds to be dates. This conclusion follows as a possibility.
Conclusion II: All dates are raisins.
As derived from combining Statement 1 ("All dates are cashews") and Statement 2 ("All cashews are raisins"), we established that All Dates are Raisins. This conclusion directly and logically follows from the given statements.
Conclusion III: No cashew is an almond.
We know that All Cashews are Raisins. We also know that Some Raisins are Almonds. The statement "Some raisins are almonds" means there is an overlap between Raisins and Almonds. This overlap could include parts of the Raisins that are also Cashews, or it might not. The statements do not provide enough information to definitively say that *no* cashew is an almond. It is possible that some cashews *are* almonds (since cashews are a subset of raisins and some raisins are almonds). Thus, the conclusion "No cashew is an almond" does not logically follow; it is not necessarily true.
Summary of Conclusion Analysis
| Conclusion | Analysis | Logically Follows? |
|---|---|---|
| I. All almonds being dates is a possibility. | Relationship between Almonds and Dates via Raisins allows for this overlap. | Yes (as a possibility) |
| II. All dates are raisins. | Directly derived from combining statements 1 & 2. | Yes |
| III. No cashew is an almond. | Statements do not preclude some cashews being almonds. | No |
Based on the analysis, only conclusions I (as a possibility) and II logically follow from the given statements.
Revision Table: Key Syllogism Rules
| Statement Type | Meaning | Example Relationship |
|---|---|---|
| All A are B | Set A is fully inside Set B. | A → B |
| Some A are B | Sets A and B have at least one element in common. | A ∩ B $\neq \emptyset$ |
| No A are B | Sets A and B have no elements in common. | A ∩ B = $\emptyset$ |
Additional Information on Syllogism Possibilities
In syllogism questions, a "possibility" conclusion follows if there is at least one way to draw the Venn diagrams (or conceptualize the sets) based on the statements such that the conclusion holds true, and there is no statement that directly contradicts this possibility. The statements only establish definite relationships; any scenario that doesn't violate these definite relationships is considered possible. In this case, the "Some Raisins are Almonds" statement allows for various overlaps between Raisins and Almonds, including the possibility that the subset of Raisins which are Dates entirely consists of Almonds, or overlaps significantly with Almonds, allowing 'All almonds being dates' as a valid possible scenario.
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.
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.
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.
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.
