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 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.
Consider the given statement(s) to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statement 1: All elephants are men.
Statement 2: All men are socks.
Conclusion I: Some socks are elephants.
Conclusion II: All elephants are socks.In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the question are represented by two classes of alphabets in two matrices given below. The columns and rows of Matrix 1 are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'A' can be represented by 04, 12, etc., and 'U' can be represented by 59, 66, etc. Similarly, you have to identify the set for the word 'ROOT'.
MATRIX I
0 1 2 3 4 0 B C D E A 1 D E A B C 2 C D E A B 3 A B C D E 4 E A B C D MATRIX II
5 6 7 8 9 5 R O N T U 6 T U R O N 7 O N T U R 8 U R O N T 9 N T U R O Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statements: 1. All fish are tortoise.
2. No tortoise is a crocodile.
Conclusion: 1. No crocodile is a fish.
II. No fish is a crocodile.
Consider the given statements to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statements: 1. All books are novels.
2. Some novels are poems.
Conclusions: I. Some books are poems.
II. Some poems are novels.Consider the statement to be true and decide which of the conclusions logically follow:
Statement:
All dogs are animals.
All animals are living beings.
Conclusion
I:Dog is not an animal.
II. Dog is an animal.In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the matrices are represented by two classes of alphabets as in two matrices given below. The columns and rows of Matrix I are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'A' can be represented by 01, 13, etc., and 'S' can be represented by 55, 66, etc. Similarly, you have to identify the set for the word 'BOTH'.
MATRIX I
0 1 2 3 4 0 F A N O I 1 I O F A N 2 A N O I F 3 O F I N A 4 N I A F O MATRIX II
5 6 7 8 9 5 S E H B T 6 H S E T B 7 B T S E H 8 E H T B S 9 T S E H B Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statement I: All astronomers are scientists.
Statement II: Some scientists are shopkeepers.
Conclusion I: All astronomers are shopkeepers.
Conclusion II: All astronomers are scientists.
Conclusion III: Some shopkeepers are astronomers.
Conclusion IV: All scientists are astronomers.A word is represented by only one set of numbers as given in any one of the options. The sets of numbers are formed using two matrices below. The rows and columns of Matrix I are numbered 0 to 4 and Matrix II are numbered 5 to 9. A letter is represented by its row and column numbers. For example, ‘G’ can be coded as 12 or 21, and ‘L’ as 76 or 67.
Find the correct code for the word ‘LIFE’.
Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement:
Statements: Some cars are caves.
Conclusion: I. Some cars are not buses
II. Some caves are buses
III. No cave is a bus
IV. Some caves are cars
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.
