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.
Both conclusions III and IV follow
Understanding Statements and Conclusions Logic
This question tests your ability to draw logical inferences based on given statements, even if those statements contradict real-world facts. We need to analyze each statement and see which of the given conclusions logically follows.
Analyzing the Given Statements
We have three statements:
- All lemons are plums. (Statement 1)
- All plums are dates. (Statement 2)
- Some dates are mangoes. (Statement 3)
Analyzing the Given Conclusions
We need to evaluate four conclusions:
- Some lemons are mangoes. (Conclusion I)
- Some mangoes are plums. (Conclusion II)
- All lemons are dates. (Conclusion III)
- Some mangoes are dates. (Conclusion IV)
Step-by-Step Evaluation of Conclusions
Evaluating Conclusion I: Some lemons are mangoes
From Statement 1, we know that the set of 'lemons' is entirely contained within the set of 'plums'. From Statement 2, we know that the set of 'plums' is entirely contained within the set of 'dates'. This means the set of 'lemons' is also entirely contained within the set of 'dates'.
Statement 3 tells us 'Some dates are mangoes'. This indicates an overlap between the set of 'dates' and the set of 'mangoes'. However, this overlap might occur in the part of 'dates' that are NOT 'lemons' (or 'plums'). There is no direct or indirect link established between 'lemons' and 'mangoes' that guarantees an overlap between these two sets.
Therefore, Conclusion I does not necessarily follow.
Evaluating Conclusion II: Some mangoes are plums
We know from Statement 2 that 'All plums are dates'. Statement 3 says 'Some dates are mangoes'. This means there is an intersection between 'dates' and 'mangoes'. However, this intersection might be in the part of 'dates' that are NOT 'plums'. For example, if 'Dates' includes categories A and B, and 'Plums' are only in category A, 'Mangoes' could overlap only with category B of 'Dates'.
There is no information that forces the overlap between 'dates' and 'mangoes' to include the specific subset of 'dates' that are 'plums'.
Therefore, Conclusion II does not necessarily follow.
Evaluating Conclusion III: All lemons are dates
Statement 1: All lemons are plums.
Statement 2: All plums are dates.
If every lemon is a plum, and every plum is a date, then it logically follows that every lemon must also be a date. This is a basic principle of syllogistic reasoning (specifically, Barbara in AAA-1 form, though knowing the name isn't necessary, the logic is key).
Representing this:
- Lemons <span>⊂</span> Plums
- Plums <span>⊂</span> Dates
- Therefore, Lemons <span>⊂</span> Dates
This means 'All lemons are dates' logically follows from Statements 1 and 2.
Evaluating Conclusion IV: Some mangoes are dates
Statement 3 says: Some dates are mangoes.
In logic, the statement 'Some A are B' implies that 'Some B are A'. If it is true that 'Some dates are mangoes', then it must also be true that 'Some mangoes are dates'. This is the rule of conversion for 'I' type propositions (Particular Affirmative).
Therefore, Conclusion IV logically follows directly from Statement 3.
Summary of Conclusions
- Conclusion I (Some lemons are mangoes): Does NOT follow.
- Conclusion II (Some mangoes are plums): Does NOT follow.
- Conclusion III (All lemons are dates): FOLLOWS.
- Conclusion IV (Some mangoes are dates): FOLLOWS.
Based on our analysis, only Conclusions III and IV logically follow from the given statements.
Revision Table: Statement Types and Conversion Rules
| Statement Type | Format | Conversion (if valid) |
|---|---|---|
| A (Universal Affirmative) | All A are B | Some B are A |
| E (Universal Negative) | No A is B | No B is A |
| I (Particular Affirmative) | Some A are B | Some B are A |
| O (Particular Negative) | Some A are not B | Not Valid (generally) |
Additional Information: Syllogisms and Logic
Statements and Conclusions questions often relate to syllogisms, which are a form of logical argument where a conclusion is drawn from two or more premises (statements). Key points to remember:
- Always assume the given statements are true, regardless of real-world knowledge.
- The conclusion must logically follow *only* from the statements provided.
- 'All A are B' means the set A is a subset of set B.
- 'Some A are B' means there is at least one element common to sets A and B.
- Drawing Venn diagrams can be helpful to visualize the relationships between the categories in the statements.
- Mastering the rules of inference and conversion helps in quickly evaluating conclusions.
In this problem, the combination of 'All lemons are plums' and 'All plums are dates' is a classic example demonstrating transitivity, leading to the conclusion 'All lemons are dates'. The conversion rule directly supports 'Some mangoes are dates' from 'Some dates are mangoes'.
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.
