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.
Only conclusions I and III follow
Understanding Logical Reasoning Syllogisms
This question falls under the category of logical reasoning, specifically dealing with syllogisms or deductive reasoning from given statements to determine valid conclusions. The key is to assume the statements are absolutely true and only derive conclusions that logically and necessarily follow from them.
Analyzing the Syllogism Statements
Let's break down the given statements:
- Statement 1: Some cards are postcards.
- Statement 2: Some cards are envelopes.
- Statement 3: All envelopes are copies.
These statements describe relationships between different categories: Cards, Postcards, Envelopes, and Copies. We can visualize these relationships using Venn diagrams or simply analyze the implications of each statement.
Evaluating the Syllogism Conclusions
Now, let's examine each conclusion based on the truth of the statements.
Conclusion I: Some copies are envelopes.
Look at Statement 3: "All envelopes are copies." This statement means that the entire set of envelopes is contained within the set of copies. If every single envelope is a copy, it necessarily follows that there exist some items within the set of copies that are envelopes (namely, all the envelopes). This is a direct and unavoidable consequence of Statement 3.
Conclusion I logically follows from the statements.
Conclusion II: Some postcards are copies.
Consider the relationships: Some cards are postcards (Statement 1), some cards are envelopes (Statement 2), and all envelopes are copies (Statement 3). We know there's an overlap between Cards and Postcards, and an overlap between Cards and Envelopes. We also know that the entire group of Envelopes is part of the Copies group.
However, the fact that some cards overlap with postcards and some cards overlap with envelopes (which are copies) does not guarantee that the 'some cards' that are postcards are the same as, or even overlap with, the 'some cards' that are envelopes. Therefore, there is no necessary connection established between Postcards and Copies based *only* on these statements. It is possible that the postcards and the copies are completely separate categories, even while satisfying the statements.
Conclusion II does not logically follow from the statements.
Conclusion III: Some cards are copies.
Consider Statement 2: "Some cards are envelopes." Now look at Statement 3: "All envelopes are copies." If there are some items that are both cards and envelopes, and every item that is an envelope is also a copy, then those very same items must be both cards and copies. If 'X' is a card and 'X' is an envelope (as per Statement 2), and if 'X' is an envelope, then 'X' is also a copy (as per Statement 3). Therefore, 'X' is a card and 'X' is a copy. This means some cards are copies.
Conclusion III logically follows from the statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I: Some copies are envelopes - Follows.
- Conclusion II: Some postcards are copies - Does not follow.
- Conclusion III: Some cards are copies - Follows.
Therefore, only conclusions I and III logically follow from the given statements.
Revision Table: Syllogism Analysis
| Statement/Conclusion | Relationship | Logical Deduction | Follows? |
|---|---|---|---|
| Statement 1 | Some Cards are Postcards | Partial overlap | N/A |
| Statement 2 | Some Cards are Envelopes | Partial overlap | N/A |
| Statement 3 | All Envelopes are Copies | Envelopes $\subset$ Copies | N/A |
| Conclusion I | Some Copies are Envelopes | Directly from Statement 3 ($\text{If E} \subset \text{C}, \text{ then some C are E}$) | Yes |
| Conclusion II | Some Postcards are Copies | No guaranteed link through Cards | No |
| Conclusion III | Some Cards are Copies | From Statement 2 & 3 ($\text{Cards } \cap \text{ Envelopes } \ne \emptyset \text{ and Envelopes } \subset \text{ Copies} \Rightarrow \text{Cards } \cap \text{ Copies } \ne \emptyset$) | Yes |
Additional Information on Syllogisms and Logic
Syllogisms are a fundamental part of deductive reasoning. They consist of premises (statements) and a conclusion. A conclusion is valid if it must be true whenever the premises are true.
- Categorical Syllogisms: These deal with statements about categories or classes of things (e.g., All A are B, Some A are B, No A are B, Some A are not B). The statements in this question are examples of such premises.
- Validity vs. Truth: In logic, we are concerned with the *validity* of the argument form, not necessarily the real-world truth of the statements. If the statements are assumed true, does the conclusion *have* to be true?
- Common Pitfalls: A common mistake is to assume relationships that are not explicitly stated or necessarily implied. For example, "Some A are B" does not imply "Some A are not B" or "All A are B". "Some A are B" and "Some B are C" does not imply "Some A are C".
- Methods: Venn diagrams are a visual tool to represent the relationships between categories and test the validity of conclusions. Alternatively, one can use logical rules and structures to derive conclusions.
Mastering syllogisms requires careful attention to the exact wording of the statements and drawing only those conclusions that are logically required.
Similar Questions
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
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 alternatives 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., 'C' can be represented by 56, 75, etc. Similarly you have to identify the set for the word 'NICE'.
Matrix I (Rows 0–4)
0 1 2 3 4 0 A B C D E 1 F G H I J 2 K L M N O 3 P Q R S T 4 U V W X Y Matrix II (Rows 5–9)
5 6 7 8 9 5 Z A B C D 6 E F G H I 7 J K L M N 8 O P Q R S 9 T U V W X The word 'NICE' is represented as follows in the matrices:
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.
