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: No boat is ship. Some ships are rods. Conclusions: I. No boat is rod. II. Some rods are ships. III. Some rods are not boats.
Solving Syllogism Logic Problems
This question requires us to analyze the relationship between different categories based on the given statements and determine which conclusions logically follow. This type of problem is common in logical reasoning tests and is often solved using Venn diagrams or by applying rules of syllogism.
Understanding the Statements and Conclusions
We are given two statements:
- Statement 1: No boat is ship.
- Statement 2: Some ships are rods.
We need to evaluate three conclusions:
- Conclusion I: No boat is rod.
- Conclusion II: Some rods are ships.
- Conclusion III: Some rods are not boats.
Analyzing the Statements Using Venn Diagrams
We can represent the categories (Boat, Ship, Rod) and their relationships using Venn diagrams:
- Statement 1: No boat is ship. This means the circle representing 'Boat' and the circle representing 'Ship' have absolutely no overlap. They are mutually exclusive.
- Statement 2: Some ships are rods. This means there is an overlap between the circle representing 'Ship' and the circle representing 'Rod'. There is a region where elements belong to both 'Ship' and 'Rod'. This "some" implies at least one, and possibly all, but not necessarily all.
Combining these, we have 'Boat' and 'Ship' separate. The 'Rod' circle overlaps with the 'Ship' circle. The 'Rod' circle's position relative to the 'Boat' circle is not directly specified, other than through its relation with 'Ship'.
Evaluating the Conclusions
Let's examine each conclusion based on our understanding from the statements and the Venn diagram visualization:
Conclusion I: No boat is rod.
From the statements, we know that 'Boat' and 'Ship' are entirely separate. We also know that some 'Ship' are 'Rod'. This overlap between 'Ship' and 'Rod' could potentially overlap with 'Boat', or it might not. The statements do not provide enough information to definitively say that 'No boat is rod'. It is possible for some 'Rod' to be 'Boat' while still satisfying the statements (e.g., if the 'Rod' circle extends into the 'Boat' circle while also overlapping 'Ship'). Therefore, this conclusion does not necessarily follow.
Conclusion II: Some rods are ships.
The second statement is "Some ships are rods". This statement directly tells us about the relationship between 'Ship' and 'Rod'. If "Some ships are rods", it logically follows that "Some rods are ships". This is a simple conversion of an 'I' type statement (Some S are P converts to Some P are S). This conclusion follows directly from Statement 2.
Conclusion III: Some rods are not boats.
We know from Statement 2 that "Some ships are rods". Let's call the set of things that are both ships and rods as (Ships $\cap$ Rods). This set is non-empty because "Some ships are rods". From Statement 1, we know that "No boat is ship". This means the set of things that are both boats and ships is empty (Boats $\cap$ Ships = $\emptyset$). Since (Ships $\cap$ Rods) is a part of Ships, and no Ship is a Boat, it must be true that none of the elements in (Ships $\cap$ Rods) are Boats. Therefore, the rods that are also ships are not boats. Since we know "Some ships are rods", this implies that there is a set of 'Some rods' that fall into the category (Ships $\cap$ Rods). These specific rods are not boats. Thus, the conclusion "Some rods are not boats" logically follows from the statements.
Summary of Conclusions
| Conclusion | Follows? | Reasoning |
|---|---|---|
| I. No boat is rod. | No | Not necessarily true based on statements; possible scenarios contradict it. |
| II. Some rods are ships. | Yes | Directly follows from the conversion of "Some ships are rods". |
| III. Some rods are not boats. | Yes | Rods that are ships cannot be boats as no boat is a ship. Since some ships are rods, some rods are not boats. |
Based on the analysis, only conclusions II and III logically follow from the given statements.
Revision Table: Syllogism Statements and Conclusions
Understanding the standard types of statements in syllogism helps in analyzing relationships:
| Type | Form | Example | Conversion |
|---|---|---|---|
| A | All S are P | All dogs are mammals. | Valid only for 'Some P are S'. |
| E | No S is P | No cats are dogs. | Valid for 'No P is S'. |
| I | Some S are P | Some students are athletes. | Valid for 'Some P are S'. |
| O | Some S are not P | Some fruits are not apples. | Generally invalid for conversion. |
In our problem:
- "No boat is ship" is an E statement (No S is P). Its conversion "No ship is boat" is also true.
- "Some ships are rods" is an I statement (Some S are P). Its conversion "Some rods are ships" is true. This confirms Conclusion II.
Additional Information: Deductive Logic and Syllogisms
Syllogism is a form of deductive reasoning where a conclusion is drawn from two given or assumed propositions (premises), which share a term with the conclusion, but not with each other. In a standard form categorical syllogism, there are three parts:
- Major premise: Links the major term (predicate of the conclusion) to the middle term.
- Minor premise: Links the minor term (subject of the conclusion) to the middle term.
- Conclusion: Links the minor term to the major term.
Our problem does not fit the strict form of a standard categorical syllogism directly, but it uses the underlying principles of logical deduction from premises. The term 'Ship' acts as a middle term connecting 'Boat' and 'Rod'. We deduce relationships between 'Boat' and 'Rod' based on their individual relationships with 'Ship'. The validity of the conclusions depends solely on the logical structure and the truth of the premises, not on external facts.
Conclusion III relies on the properties of sets. The set of 'Rods' contains a subset that overlaps with 'Ships'. This overlapping subset (Rods that are also Ships) cannot contain any 'Boats' because the set of 'Ships' and the set of 'Boats' have no overlap. Therefore, the rods in that specific subset are not boats, confirming that 'Some rods are not boats'.
Similar Questions
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:
All chairs are cupboards.
Some chairs are radios.
No chair is piano.
Conclusions:
I. Some radios are cupboards.
II. Some cupboards are not piano.
III. Some radios are not piano.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, 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 aero-planes are cars.
All helicopters are cars.
All cars are scooters.
Conclusions:
1. All helicopters are scooters.
2. Some aero-planes are helicopters.
3. No aero-plane is helicopter.
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 books are grapes.
Some grapes are fruits.
Conclusions:
I. No grape is a book.
II. Some grapes are books.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 fans are radio.
All fans are light.
Conclusion I: Some radios are light.
Conclusion II: Some lights are radio.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 scissors are spoons.
All spoons are plates.
Conclusions:
1. Some plates are spoons.
2. Some spoons are scissors.
3. Some plates are scissors.
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 bottles are glasses.
All glasses are jugs.
Conclusions:
I. All bottles are jugs.
II. All jugs are bottles.
III. Some glasses are bottles.
In the following question below are given some statements followed by some conclusions. 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 pen are black.
II. Some pen are blue.
III. No black is red.
Conclusions:
I. No pen is red.
II. Some blue are black.
III. Some black are pens.In the following question below are given some statements followed by some conclusions. 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. All cups are plates.
II. All plates are red.
Conclusions:
I. All cups are red.
II. All plates are cups.
III. All red are plates.In the following question below are given some statements followed by some conclusions. 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 sky are blue.
II. Some blue are soft.
Conclusions:
I. Some sky are soft.
II. Some soft are sky.What will come in the place of the question mark (?) in the following equation if '+' and '-' are interchanged and 'x' and '÷' are interchanged?
108 × 2 − 14 ÷ 6 + 27 = ?
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.
