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: All tools are spanners. Some spanners are utensils. No spanner is an iron. Conclusions: (I) Some tools are irons. (II) Some utensils are tools. (III) Some utensils are not iron.
Only conclusion III follows
Solving Syllogism Statements and Conclusions
This question asks us to analyze three statements and determine which of the given conclusions logically follow from them. We must assume the statements are true, even if they contradict common knowledge. This type of problem is known as a syllogism, a form of deductive reasoning.
Understanding the Statements
Let's break down the given statements:
- Statement 1: All tools are spanners. (Relationship: Tools → Spanners. All members of the 'tools' category are also members of the 'spanners' category.)
- Statement 2: Some spanners are utensils. (Relationship: Spanners ↔ Utensils. There is at least one spanner that is a utensil, and at least one utensil that is a spanner. Note: This also implies some spanners may *not* be utensils, and some utensils may *not* be spanners, but we only know for sure about the overlap.)
- Statement 3: No spanner is an iron. (Relationship: Spanners ↔ Iron. There is absolutely no overlap between the 'spanners' category and the 'iron' category.)
Analyzing Conclusions Using Statements
We will now evaluate each conclusion based on the provided statements.
Conclusion I: Some tools are irons.
Let's look at the statements relevant to Tools and Irons:
- Statement 1: All tools are spanners.
- Statement 3: No spanner is an iron.
Since all tools are contained within the category of spanners (Statement 1), and the category of spanners has no overlap whatsoever with the category of irons (Statement 3), it logically follows that the category of tools also has no overlap with the category of irons. If no spanner is iron, and every tool is a spanner, then no tool can be an iron.
Therefore, the conclusion "Some tools are irons" contradicts the logical deduction from the statements. This conclusion does not follow.
Conclusion II: Some utensils are tools.
Let's look at the statements relevant to Utensils and Tools:
- Statement 1: All tools are spanners.
- Statement 2: Some spanners are utensils.
Statement 2 tells us there is an overlap between Spanners and Utensils. Statement 1 tells us that the 'Tools' category is a subset of the 'Spanners' category. The 'some spanners' that are utensils (from Statement 2) could be spanners that are *not* tools, or they could be spanners that *are* tools, or a combination. From the statements alone, we cannot definitively say that the overlapping group of 'spanners that are utensils' includes any tools. The 'some spanners' could be entirely outside the 'Tools' circle within the 'Spanners' circle.
Therefore, we cannot logically conclude that "Some utensils are tools" from the given statements. This conclusion does not follow.
Conclusion III: Some utensils are not iron.
Let's look at the statements relevant to Utensils and Irons:
- Statement 2: Some spanners are utensils.
- Statement 3: No spanner is an iron.
Statement 2 tells us there is a group of items that are both spanners and utensils. Let's call this group X. So, X consists of items that are "spanners which are utensils".
Statement 3 tells us that "No spanner is an iron". This means anything that is a spanner cannot be an iron.
Since the group X consists of spanners (as they are "spanners which are utensils"), and we know that no spanner is an iron, it must be true that the items in group X (the utensils that are spanners) are not iron.
Thus, there exists a group of utensils (those that are also spanners) that are not iron. Therefore, the conclusion "Some utensils are not iron" logically follows from the statements.
Summary of Conclusions
Based on the analysis:
- Conclusion I: Some tools are irons. - Does not follow.
- Conclusion II: Some utensils are tools. - Does not follow.
- Conclusion III: Some utensils are not iron. - Follows.
Only conclusion III logically follows from the given statements.
| Statement | Type | Relationship |
|---|---|---|
| All tools are spanners. | Universal Affirmative (A) | Tools → Spanners |
| Some spanners are utensils. | Particular Affirmative (I) | Spanners ↔ Utensils (Partial Overlap) |
| No spanner is an iron. | Universal Negative (E) | Spanners ↔ Iron (No Overlap) |
| Conclusion | Analysis | Follows? |
|---|---|---|
| (I) Some tools are irons. | Tools are subset of Spanners; Spanners are separate from Irons. Thus, Tools are separate from Irons. | No |
| (II) Some utensils are tools. | Some Spanners are Utensils; Tools are subset of Spanners. The Utensils-Spanners overlap might be outside Tools area. | No |
| (III) Some utensils are not iron. | Some Utensils are Spanners; No Spanner is Iron. The Utensils that are Spanners cannot be Iron. | Yes |
Revision Table: Key Concepts in Syllogism
| Term | Explanation |
|---|---|
| Statement | A premise providing a relationship between categories. |
| Conclusion | A deduction derived from the statements. |
| Syllogism | A type of logical argument where a conclusion is inferred from two or more statements (premises). |
| Follows Logically | The conclusion must be true if the statements are true. |
| Universal Affirmative (All A are B) | Every member of category A is a member of category B. |
| Particular Affirmative (Some A are B) | At least one member of category A is a member of category B. |
| Universal Negative (No A are B) | No member of category A is a member of category B. |
| Particular Negative (Some A are not B) | At least one member of category A is not a member of category B. |
Additional Information: Syllogism Solving Methods
Syllogism problems can often be solved using different methods, such as Venn Diagrams or rules of logic. Both methods aim to determine the validity of conclusions based on the given statements.
Venn Diagram Method
This method involves drawing overlapping circles to represent the categories mentioned in the statements. The relationships described by the statements are depicted by shading or marking areas within the circles. By examining the resulting diagram, one can see which conclusions are supported.
- 'All A are B' → Draw circle A completely inside circle B.
- 'Some A are B' → Draw overlapping circles for A and B, mark the overlapping region.
- 'No A is B' → Draw separate circles for A and B.
For 'Some A are not B', draw overlapping circles, mark the part of A that is outside B.
Analytical Method (Using Rules)
This method uses established rules of logic regarding the combination of different types of statements (A, E, I, O) to derive valid conclusions. This method can be more formal but requires memorizing rules about subject, predicate, middle term, distribution, etc.
For example, a Universal Affirmative (A) statement like 'All tools are spanners' and a Universal Negative (E) statement like 'No spanner is iron' can lead to a Universal Negative (E) conclusion 'No tool is iron', provided the middle term ('spanner') is distributed in at least one premise. In our case, 'spanner' is the middle term and is distributed in 'No spanner is iron'. Thus, 'No tool is iron' follows, which makes 'Some tools are irons' false.
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 pens are newspapers.
Some newspapers are novels.
No novel is a book.
Conclusions:
I. Some books are pens.
II. Some novels are pens.
III. No book is a pen.
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.
In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
I. No streak is a line.
II. Some lines are bands.
III. All bands are flashes.
Conclusions:
I. Some flashes are streaks.
II. No flash is a line.
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.
Select the Venn diagram that best illustrates the relationship between the following classes.
Swimming, Running, Sports
Select the Venn diagram that best illustrates the relationship between the following classes.
Dialect, Language, Communication
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 seeds are fruits.
Some fruits are jams.
All jams are desserts.
Conclusions:
I. Some jams are seeds.
II. Some desserts are jams.
III. Some fruits are desserts.
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 stars are moons.
Some moons are suns.
All suns are satellites.
Conclusions :
I. Some satellites are moons.
II. Some satellites are stars.
III. Some moons are stars.
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.
