The statements below are followed by four conclusions labelled I, II, III and IV. 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: No laptop is notebook. All notebooks are tablets. Conclusions: I. No laptop is tablets. II. No tablets is laptop. III. Some tablets are notebooks. IV. All the tablets are notebooks.
Only conclusion (III) follows.
Syllogism Logic: Analyzing Statements and Conclusions
This question asks us to analyze two statements and determine which of the given conclusions logically and definitely follow from these statements. We must assume the statements are true, even if they contradict common knowledge.
Analyzing the Statements
Let's break down the given statements:
- Statement 1: No laptop is notebook. This establishes a complete separation between the category 'laptop' and the category 'notebook'. There is absolutely no overlap between these two groups.
- Statement 2: All notebooks are tablets. This means that every single item that is a 'notebook' is also a 'tablet'. The category 'notebook' is entirely contained within the category 'tablet'.
We can visualize this using a simple mental model or Venn diagrams (though we won't draw them here). The 'Notebook' circle is completely inside the 'Tablet' circle. The 'Laptop' circle is entirely separate from the 'Notebook' circle.
Evaluating the Conclusions
Now let's evaluate each conclusion based on our understanding of the statements:
- Conclusion I: No laptop is tablets.
We know 'No laptop is notebook'. We also know 'All notebooks are tablets'. Does this mean no laptop can be a tablet? Not necessarily. The statements don't tell us anything about laptops and tablets directly, other than that laptops are not the specific type of tablets that are notebooks. There could be other types of tablets besides notebooks, and laptops might or might not overlap with those other types of tablets. Therefore, this conclusion does not logically follow from the given statements.
- Conclusion II: No tablets is laptop.
This conclusion is essentially the same as Conclusion I, just rephrased. If 'No laptop is tablets' doesn't follow, then 'No tablets is laptop' also doesn't logically follow for the same reasons. There is no information preventing tablets (that are not notebooks) from being laptops. Therefore, this conclusion does not logically follow from the given statements.
- Conclusion III: Some tablets are notebooks.
Statement 2 says 'All notebooks are tablets'. If every single notebook is a tablet, then it must be true that there are some items within the category 'tablets' that are also 'notebooks'. This is a fundamental inference in logic: if all of A are B, then some of B must be A (provided A is not an empty set, which we assume in these puzzles). Therefore, this conclusion logically and definitely follows from the given statements.
- Conclusion IV: All the tablets are notebooks.
Statement 2 says 'All notebooks are tablets', meaning notebooks are a subset of tablets. This does not imply that tablets are a subset of notebooks. There could be tablets that are not notebooks (e.g., a tablet that is not designed as a notebook). The statement 'All notebooks are tablets' does not provide information to support this conclusion. Therefore, this conclusion does not logically follow from the given statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I: Does not follow.
- Conclusion II: Does not follow.
- Conclusion III: Logically follows.
- Conclusion IV: Does not follow.
Thus, only conclusion (III) follows from the given statements.
| Statement/Conclusion | Analysis | Follows? |
|---|---|---|
| Statement 1: No laptop is notebook. | Laptop and Notebook are disjoint sets. | N/A |
| Statement 2: All notebooks are tablets. | Notebook set is a subset of Tablet set. | N/A |
| Conclusion I: No laptop is tablets. | Does not rule out Laptop being a Tablet (if not a Notebook). | No |
| Conclusion II: No tablets is laptop. | Same as Conclusion I, from Tablets perspective. | No |
| Conclusion III: Some tablets are notebooks. | Directly inferred from "All Notebooks are Tablets". | Yes |
| Conclusion IV: All the tablets are notebooks. | Incorrect reversal of "All Notebooks are Tablets". | No |
Final Answer Derivation
Comparing our findings with the options, the option that states "Only conclusion (III) follows" is the correct one.
Revision Table: Key Concepts in Syllogism
| Term | Explanation | Example Inference |
|---|---|---|
| Statement | A premise assumed to be true for the purpose of logical deduction. | e.g., All A are B. |
| Conclusion | A proposition derived from the statements. Must logically follow. | e.g., Some B are A (from All A are B). |
| "All A are B" | Every member of category A is also a member of category B. B is a superset of A. | Implies "Some A are B" and "Some B are A". |
| "No A is B" | Category A and Category B have no members in common. They are disjoint sets. | Implies "No B is A". |
| "Some A are B" | There is at least one member that belongs to both category A and category B. | Does NOT imply "All A are B" or "No A is B". |
Additional Information: Syllogism Reasoning
Syllogism questions are a common type of logical reasoning problem. They test your ability to deduce conclusions based purely on given premises, ignoring any outside information. The key is to follow the logic strictly from the statements provided. Using visual aids like Venn diagrams can often help clarify the relationships between the categories mentioned in the statements. Remember that "some" in logic means "at least one". Also, be careful not to assume the converse or inverse of a statement is true unless it is explicitly stated or logically follows (e.g., "All A are B" does not mean "All B are A").
Similar Questions
Read the given statements and conclusions carefully. Assuming that the information given in the statements are 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:
1. All colours are reds.
2. Some reds are greens.
3. All greens are dark.
Conclusions:
I. All colours being dark is a possibility
II. Some reds are dark.
III. Some reds are colours.
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 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.
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:
Some tents are cones.
All the cones are motels.
Conclusions:
All the motels are cones.
Some tents are motels.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 cats are hens.
All hens are goat.
Conclusions:
Conclusion I: Some hens are cat.
Conclusion II: Some goats are hens.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 pictures are prizes.
Some prizes are erasers.
Some erasers are helmets.
Conclusions:
I. Some helmets are Prizes.
II. Some erasers are pictures.
III. No helmet is a Prize.
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.
