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 spices are medicines. All medicines are chemicals. No chemical is cheap. Conclusions: I. Some medicines are cheap. II. Some chemicals are spices. III. No medicine is cheap.
Only conclusions II and III follow.
Analyzing Statements and Conclusions in Logical Reasoning
This problem requires us to evaluate which conclusions logically follow from a given set of statements, assuming the statements are true. This type of question falls under the category of logical reasoning, specifically syllogisms.
Understanding the Statements
We are given three statements:
- Statement 1: Some spices are medicines.
- Statement 2: All medicines are chemicals.
- Statement 3: No chemical is cheap.
Evaluating the Conclusions
We need to check each conclusion based on the given statements.
Conclusion I: Some medicines are cheap.
Let's analyze this based on the statements:
- Statement 2 says "All medicines are chemicals."
- Statement 3 says "No chemical is cheap."
If all medicines are chemicals, and none of the chemicals are cheap, then it logically follows that none of the medicines can be cheap. Therefore, the conclusion "Some medicines are cheap" directly contradicts the information derived from the statements.
Conclusion I does not follow.
Conclusion II: Some chemicals are spices.
Let's analyze this based on the statements:
- Statement 1 says "Some spices are medicines." This means there is at least one spice that is also a medicine.
- Statement 2 says "All medicines are chemicals." This means everything that is a medicine is also a chemical.
Since there are some spices that are medicines (Statement 1), and all medicines are chemicals (Statement 2), these 'some spices' that are medicines must also be chemicals. Therefore, some spices are chemicals. If some spices are chemicals, it logically follows that some chemicals are spices.
Conclusion II follows.
Conclusion III: No medicine is cheap.
Let's analyze this based on the statements:
- Statement 2 says "All medicines are chemicals."
- Statement 3 says "No chemical is cheap."
If every single medicine belongs to the category of chemicals (Statement 2), and nothing in the category of chemicals is cheap (Statement 3), then nothing in the category of medicines can be cheap either. This means "No medicine is cheap."
Conclusion III follows.
Summary of Conclusions
Based on the analysis:
- Conclusion I: Some medicines are cheap. (Does not follow)
- Conclusion II: Some chemicals are spices. (Follows)
- Conclusion III: No medicine is cheap. (Follows)
Therefore, only conclusions II and III logically follow from the given statements.
Revision Table: Syllogism Analysis
| Statement/Conclusion | Relationship | Analysis based on given Statements | Follows? |
|---|---|---|---|
| Statement 1 | Some Spices are Medicines (S → M) | Given | - |
| Statement 2 | All Medicines are Chemicals (M → C) | Given | - |
| Statement 3 | No Chemical is Cheap (C → Not Cheap) | Given | - |
| Conclusion I | Some Medicines are Cheap (M → Cheap) | All M are C, No C is Cheap → No M is Cheap. Contradicts conclusion. | No |
| Conclusion II | Some Chemicals are Spices (C → S) | Some S are M, All M are C → Some S are C → Some C are S. | Yes |
| Conclusion III | No Medicine is Cheap (M → Not Cheap) | All M are C, No C is Cheap → No M is Cheap. | Yes |
Additional Information on Syllogisms
Syllogisms are a form of deductive reasoning where a conclusion is drawn from two or more premises (statements). Understanding the relationship between categories described in the statements is key.
- Universal Affirmative (All A are B): Every member of category A is also a member of category B.
- Universal Negative (No A is B): No member of category A is a member of category B.
- Particular Affirmative (Some A are B): At least one member of category A is also a member of category B. 'Some' means 'at least one' and can include 'all'.
- Particular Negative (Some A are not B): At least one member of category A is not a member of category B.
Visual aids like Venn diagrams can often help represent the relationships between categories and verify conclusions. In this problem, the relationships are:
- Some Spices overlap with Medicines.
- The entire set of Medicines is inside the set of Chemicals.
- The set of Chemicals and the set of Cheap things have no overlap.
Combining these: Since Medicines are inside Chemicals, and Chemicals don't overlap with Cheap, Medicines cannot overlap with Cheap. Also, since Some Spices overlap with Medicines, and Medicines are inside Chemicals, that overlap of Spices and Medicines must also be within Chemicals, meaning Some Spices are Chemicals, and thus Some Chemicals are Spices.
Similar Questions
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 follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 oranges are apples.
Some oranges are bananas.
All bananas are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are bananas.
III. Some oranges are fruits.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some Z are X.
II. Some W are Z.
Conclusions:
I. Some X are not W.
II. Some X are not Z.
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 mobiles are flat.
All flats are TVs.
Some TVs are plastic.
Conclusions:
I. Some mobiles are TVs.
II. Some flats are plastic.
III. All plastic are TVs.
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:
No cup is a plate.
All cups are utensils.
Some bottles are cups.
Conclusions:
I. Some utensils are not plates.
II. Some bottles are not plates.
III. No bottle is a plate.
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 variance with commonly known facts. Decide which of the given conclusions logically follow/s from the given statements.
Statements:
Some watches are projectors.
All projectors are lamps.
Some heaters are watches.
Conclusions:
(I) Some heaters are projectors.
(II) Some lamps are heaters.
(III) All watches are lamps
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. No A is B.
II. No C is B.
Conclusion:
I. Some C are not A.
II. Some A are B.
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 benches are tables.
Some tables are chairs.
Some chairs are pencils.
Conclusions:
I. Some benches are chairs.
II. Some tables are pencils.
III. Some pencils are chairs.
IV. Some pencils are tables.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. No tyre are white.
II. All grey are white.
Conclusions:
I. No white is tyre.
II. No tyre is grey.
III. Some white are not grey.
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.
