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.
Only conclusion II follows.
Solving Logic Puzzles: Statements and Conclusions
Logic puzzles involving statements and conclusions test your ability to deduce information based purely on the given statements, even if they contradict general knowledge. The key is to follow the logic strictly from the premises.
Let's break down the given problem with the statements and conclusions about books, grapes, and fruits.
Understanding the Statements
We have two statements:
- All books are grapes.
- Some grapes are fruits.
Let's analyze each statement carefully:
- Statement 1: "All books are grapes." This tells us that the entire set of 'books' is contained within the set of 'grapes'. If something is a book, it is definitely a grape. This also implies that there are no books that are not grapes. From this, we can logically infer that at least some grapes are books (specifically, all the grapes that happen to be books).
- Statement 2: "Some grapes are fruits." This means there is an overlap between the set of 'grapes' and the set of 'fruits'. There is at least one grape that is also a fruit. This statement does not give us any information about all grapes, or all fruits, or any relationship between books and fruits.
Analyzing the Conclusions
Now let's evaluate the two conclusions based on our understanding of the statements.
Conclusion I: No grape is a book.
- This conclusion states that there is no overlap between the set of 'grapes' and the set of 'books'.
- However, Statement 1 explicitly says "All books are grapes". If all books are grapes, then it is impossible for *no* grape to be a book. The very grapes that are books contradict this conclusion.
- Therefore, Conclusion I does not logically follow from the statements. In fact, it directly contradicts the inference drawn from Statement 1.
Conclusion II: Some grapes are books.
- This conclusion states that there is at least one grape that is also a book.
- Let's revisit Statement 1: "All books are grapes." This means every single item belonging to the category 'book' is also an item belonging to the category 'grape'.
- If all books are grapes, then the set of books is a part of the set of grapes. This necessarily means that some members of the set 'grapes' are the members of the set 'books' (specifically, all the books).
- This is a standard inference in logic: If 'All A are B', then 'Some B are A' is a valid conclusion (assuming A is not an empty set, which is standardly assumed in these puzzles).
- Therefore, Conclusion II logically follows from Statement 1.
Putting it Together: Which Conclusion(s) Follow?
Based on our analysis:
- Conclusion I ("No grape is a book") is false according to Statement 1.
- Conclusion II ("Some grapes are books") is true according to Statement 1.
The second statement ("Some grapes are fruits") does not affect the relationship between grapes and books, so it doesn't change the validity of either conclusion regarding books and grapes.
Thus, only Conclusion II logically and definitely follows from the given statements.
Summary Table
| Statement/Conclusion | Relationship | Analysis | Follows? |
|---|---|---|---|
| Statement 1 | All books are grapes | Books are a subset of Grapes. Implies some Grapes are Books. | N/A (Premise) |
| Statement 2 | Some grapes are fruits | Overlap between Grapes and Fruits. Irrelevant to Books & Grapes relationship. | N/A (Premise) |
| Conclusion I | No grape is a book | Contradicts Statement 1's implication (Some Grapes are Books). | No |
| Conclusion II | Some grapes are books | Directly follows from Statement 1 (All Books are Grapes implies Some Grapes are Books). | Yes |
Revision Table: Key Logic Concepts
| Concept | Explanation | Example |
|---|---|---|
| Universal Affirmative (All A are B) | Every member of set A is also a member of set B. | All dogs are mammals. |
| Particular Affirmative (Some A are B) | At least one member of set A is also a member of set B. | Some students are athletes. |
| Particular Negative (Some A are not B) | At least one member of set A is not a member of set B. | Some cats are not friendly. |
| Universal Negative (No A is B) | No member of set A is a member of set B. The sets are disjoint. | No fish are birds. |
| Inference: All A are B > Some B are A | If everything in A is in B, then the items in B that are also in A constitute 'some' B. | All squares are rectangles > Some rectangles are squares. |
Additional Information: Solving Syllogisms
Syllogisms are a type of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. You can often visualize these relationships using Venn diagrams, which can help in checking the validity of conclusions.
- Draw circles representing each category (Books, Grapes, Fruits).
- "All books are grapes" means the 'Books' circle is completely inside the 'Grapes' circle.
- "Some grapes are fruits" means the 'Grapes' and 'Fruits' circles overlap.
- Then, check if the conclusions hold true based on your diagram. For "No grape is a book", look if the 'Grapes' and 'Books' circles are separate (they are not, 'Books' is inside 'Grapes'). For "Some grapes are books", look if there is any part of the 'Grapes' circle that is also part of the 'Books' circle (yes, the entire 'Books' circle which is inside 'Grapes').
This visual method confirms that Conclusion II follows, while Conclusion I does not.
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 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.
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.
