All questions of Syllogism for Mechanical Engineering Exam

Statements :
All tables are wood. No wood is a metal. Some metals are glasses.
Conclusions :
I.No Table is a metal
II.Some glasses are table
  • a)
    If only conclusion I follows.
  • b)
    If only conclusion II follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'A'. Can you explain this answer?

Pankaj Nambiar answered

Explanation:

- All tables are wood. This statement tells us that all tables are made of wood.
- No wood is a metal. This statement tells us that wood and metal are mutually exclusive categories.
- Some metals are glasses. This statement tells us that there is an overlap between metals and glasses.

Conclusion I: No Table is a metal
- Since all tables are wood and no wood is a metal, it can be concluded that no table is a metal. This conclusion directly follows from the given statements.

Conclusion II: Some glasses are table
- While some metals are glasses, there is no direct relationship established between glasses and tables in the given statements. Therefore, this conclusion cannot be inferred from the given premises.

Therefore, the correct answer is option 'A' - If only conclusion I follows.

Statements : All words are letters. All vowels are letters. Some vowels are alphabets.
Conclusions :
I.No word is a vowel
II.Some letters being alphabets is a possibility
  • a)
    If only conclusion I follows.
  • b)
    If only conclusion II follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'B'. Can you explain this answer?

Prashanth Jain answered
Statements:
- All words are letters.
- All vowels are letters.
- Some vowels are alphabets.

Conclusions:
I. No word is a vowel.
II. Some letters being alphabets is a possibility.

Explanation:
- The given statements suggest that all words and vowels are a type of letter, and some vowels are also alphabets.
- Conclusion I, "No word is a vowel", is incorrect as some words can be vowels as well (e.g. "I", "a").
- Conclusion II, "Some letters being alphabets is a possibility", is correct as the given statements establish that some vowels are also alphabets.
- Therefore, the correct answer is option B, "If only conclusion II follows".

Statements :
All pens are pencils. Some erasers are pencils. All Scales are pens.
Conclusions :
I.All scales are pencils
II.All erasers being scale is a possibility.
  • a)
    If only conclusion I follows.
  • b)
    If only conclusion II follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'E'. Can you explain this answer?

Statements and Conclusions:

Statements:
- All pens are pencils.
- Some erasers are pencils.
- All scales are pens.

Conclusions:
I. All scales are pencils.
II. All erasers being scale is a possibility.

Explanation:
From the given statements, we can conclude that:
- All pens are pencils.
- Some erasers are pencils.
- All scales are pens, which means all scales are pencils as well.

Therefore, conclusion I follows logically from the given statements.

For conclusion II, we need to analyze the given statements carefully. It is given that "Some erasers are pencils" and "All pens are pencils". This means that there are some erasers which are also pencils, and since all pens are pencils, some pens must also be erasers. Hence, it is possible that some erasers are scales. Therefore, conclusion II also follows logically from the given statements.

Hence, both conclusions I and II follow from the given statements.

Answer: Option E (If both conclusions I and II follow).

Statements
All plants are flowers
Some flowers are roses
Conclusion:
I.Some roses are plants
II.No rose is plant
  • a)
    If only conclusion I follows.
  • b)
    If only conclusion II follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'C'. Can you explain this answer?

Varun Rane answered
Explanation:

Given Statements:
- All plants are flowers
- Some flowers are roses

Conclusion I:
- Some roses are plants
- This conclusion can be derived from the given statements. Since all plants are flowers and some flowers are roses, it is reasonable to conclude that some roses are plants.

Conclusion II:
- No rose is plant
- This conclusion cannot be concluded from the given statements. The statements only mention that some flowers are roses, but it does not provide enough information to determine whether no rose is a plant.

Therefore, the correct answer is:
- If either I or II follows. This means that conclusion I can be derived from the given statements, while conclusion II cannot be definitively determined.

Statements : No score is a mark. All marks are percentages. Some grades are percentages.
Conclusions :
I.All grades being marks is a possibility
II.No mark is a score
  • a)
    If only conclusion I follows.
  • b)
    If only conclusion II follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'E'. Can you explain this answer?

Analysis:
Considering the given statements and conclusions, let's analyze them one by one to determine their validity.

Statement Analysis:
- No score is a mark: This statement implies that scores and marks are different entities.
- All marks are percentages: This statement indicates that all marks are represented in percentages.
- Some grades are percentages: This statement suggests that there are grades that are expressed in percentages.

Conclusion Analysis:
I. All grades being marks is a possibility
- This conclusion can be drawn from the fact that all marks are percentages, and some grades are percentages. It is possible for grades to also be considered as marks, given their interrelation with percentages.
II. No mark is a score
- This conclusion can be derived from the statement "No score is a mark," which implies that scores and marks are mutually exclusive.

Conclusion:
Both conclusions I and II are valid based on the given statements. Grades can be considered as marks since they are related to percentages, and scores are distinct from marks according to the statements provided. Therefore, the correct answer is option 'E,' where both conclusions follow logically.

Statements : Some papers are covers. No cover is a book. All books are pages
Conclusions :
At least some papers are not book
No book is a cover
  • a)
    If only conclusion I follows.
  • b)
    If only conclusion II follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'E'. Can you explain this answer?

Krithika Bose answered
Statements:
- Some papers are covers.
- No cover is a book.
- All books are pages.

Conclusions:
- At least some papers are not book.
- No book is a cover.

Explanation:
- From the first statement, we can infer that there is a possibility that some papers may not be covers.
- From the second statement, we can infer that covers and books are mutually exclusive categories.
- From the third statement, we can infer that all books are pages.

Conclusion I:
- As there is a possibility of papers that are not covers, it is possible that some papers are not books. Hence, conclusion I follows.

Conclusion II:
- As per the given statements, it is clear that no cover is a book. Hence, conclusion II also follows.

Therefore, both conclusions I and II follow.

Final Answer:
- Option E (If both conclusions I and II follow)

Statements :
Some pens are paper
Eraser is a pen
Conclusion:
I.Eraser is not a paper
II.Eraser is a paper
  • a)
    If only conclusion I follows.
  • b)
    If only conclusion II follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'C'. Can you explain this answer?

Shruti Reddy answered
Statements:
- Some pens are paper.
- Eraser is a pen.

Conclusion:
I. Eraser is not a paper.
II. Eraser is a paper.

Explanation:
To determine whether the conclusions follow from the given statements, let's analyze each conclusion separately.

Conclusion I: Eraser is not a paper.
- The first statement states that some pens are paper. This means that there is at least one pen that is made of paper.
- The second statement declares that an eraser is a pen.
- Combining these statements, we can conclude that since an eraser is a pen, it cannot be made of paper. Therefore, conclusion I follows.

Conclusion II: Eraser is a paper.
- This conclusion contradicts the first statement which states that some pens are paper. If an eraser is a pen, it cannot be a paper.
- Therefore, conclusion II does not follow.

Final Answer:
Therefore, only conclusion I follows, and the correct answer is option 'C' - If either I or II follows.

Statements: All A are B. Some B are C. All C are D.
Conclusions: –  1) All D are C. 2) All D are A. 3) Some D are B.
  • a)
    Only 1 follow
  • b)
    Only 2 follow
  • c)
    Only 3 follow
  • d)
    all follow.
Correct answer is option 'C'. Can you explain this answer?

Let's analyze each conclusion one by one in relation to the given statements:

All D are C: This conclusion cannot be derived from the given statements. The statements state that "All C are D," which means every element of C is also an element of D. However, this does not imply that every element of D is an element of C. Therefore, conclusion 1 does not follow.

All D are A: This conclusion cannot be derived from the given statements. The statements state that "All A are B" and "Some B are C," but they do not provide any direct relationship between A and D. Therefore, conclusion 2 does not follow.

Some D are B: This conclusion can be derived from the given statements. The statements state that "All C are D" and "Some B are C." If some B are C, and all C are D, then it is possible for some D to be B. Therefore, conclusion 3 follows.

Hence, the correct answer is option 'C' Only conclusion 3 follows.

Statements :
All stars are moons. All moons are sun. All asteroids are sun.
Conclusions :
I.Some moons are asteroids.
II.All stars are sun
  • a)
    If only conclusion I follows.
  • b)
    If only conclusion II follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'B'. Can you explain this answer?

Explanation:

  • All stars are moons and all moons are sun, so all stars and moons are also sun.

  • All asteroids are sun, but it does not mean that all asteroids are moons or stars.

  • Therefore, the conclusion II "All stars are sun" is correct, as all stars are also sun.

  • However, the conclusion I "Some moons are asteroids" is not necessarily true, as there is no direct relation between moons and asteroids in the given statements. It is possible that there could be some moons that are asteroids, but it is not necessarily true.

  • Hence, the correct answer is option B - If only conclusion II follows.

Statements: Some actors are singers. All the singers are dancers:
Conclusions:
a. Some actors are dancers.
b. No singer is actor.
  • a)
    If only conclusion II follows. 
  • b)
    If only conclusion I follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'B'. Can you explain this answer?

Rajat Saha answered
Statement and Conclusion in LR

Statement: Some singers are actors. Some actors are dancers.

Conclusion I: Some dancers are definitely not actors.

Conclusion II: Some dancers being singers is a possibility.

Explanation:

To solve this question, we need to analyze the given statements and check whether the conclusions follow or not.

From the given statements, we can derive the following Venn diagram:

Singers (A) <--> Actors (B) <--> Dancers (C)

Now, let's analyze the conclusions one by one:

Conclusion I: Some dancers are definitely not actors.

From the given Venn diagram, we can see that there is a possibility that some dancers may not be actors. Hence, this conclusion follows.

Conclusion II: Some dancers being singers is a possibility.

From the given Venn diagram, we can see that there is a possibility that some dancers may also be singers. Hence, this conclusion also follows.

Therefore, the correct answer is option B - If only conclusion II follows.

Conclusion:

In this question, we have used logical reasoning to analyze the given statements and derive the correct conclusions. It is important to carefully read the statements and use logical thinking to arrive at the correct answer.

Statements:
All fashionable are addicts.
All addicts are noteworthy.
Conclusions:
I. No noteworthy is fashionable.
II. Some noteworthy are fashionable
  • a)
    if only conclusion I follows.
  • b)
    if only conclusion II follows.
  • c)
    if either I or II follows.
  • d)
    if neither I nor II follows.
  • e)
    if both conclusions I and II follow.
Correct answer is option 'B'. Can you explain this answer?

Priya Reddy answered
Explanation:
All fashionable are addicts:
- This statement implies that every fashionable person is also an addict.
All addicts are noteworthy:
- This statement means that every addict is noteworthy.

Conclusions:
I. No noteworthy is fashionable:
- This conclusion is not valid because the statements do not provide any information about the relationship between noteworthy individuals and fashionable individuals. It cannot be definitively concluded that no noteworthy person is fashionable based on the given statements.
II. Some noteworthy are fashionable:
- This conclusion is valid. Since all addicts are noteworthy and all fashionable people are addicts, it is possible that some noteworthy individuals may also be fashionable. There is a possibility of overlap between the two groups.
Therefore, the correct answer is option B as only conclusion II follows logically from the given statements.

Statements :
All letters are consonants. All alphabets are letters. All words are alphabets
Conclusions :
I.All words are consonants
II.Some letters are not words
  • a)
    If only conclusion I follows.
  • b)
    If only conclusion II follows.
  • c)
    If either I or II follows.
  • d)
    If neither I nor II follows.
  • e)
    If both conclusions I and II follow.
Correct answer is option 'A'. Can you explain this answer?

Abhiram Patel answered
To determine if the given conclusions follow from the statements, let's analyze each conclusion separately:

Conclusion I: All words are consonants.
- According to the given statements, all letters are consonants. Therefore, if all letters are consonants and all alphabets are letters, it can be concluded that all alphabets are consonants.
- However, there is no direct information given about words in the statements. So, we cannot definitively conclude that all words are consonants based on the given information.

Conclusion II: Some letters are not words.
- According to the given statements, all letters are consonants. This implies that all letters are part of the set of consonants.
- Since the set of letters includes all alphabets and all words are alphabets, it can be concluded that all letters are also part of the set of words.
- Therefore, it is not possible to have any letters that are not words based on the given information.
- Thus, conclusion II does not follow from the statements.

In summary, only conclusion I follows from the given statements. Therefore, the correct answer is option 'A' - If only conclusion I follows.

Statements:
No leopard is a cheetah.
Some cheetahs are tigers.
All tigers are lions.
Conclusions:
I.Some leopards are not tigers.
II.All leopards are tigers.
  • a)
    If only conclusion I follows.
  • b)
    If only conclusions II follows.
  • c)
    If either conclusion I or II follows.
  • d)
    If neither conclusion I nor II follows.
  • e)
    If both conclusion I and II follow.
Correct answer is option 'C'. Can you explain this answer?

Priya Reddy answered
No leopard is a cheetah. Some cheetahs are tigers. All tigers are lions.

Let's evaluate the given statements and conclusions:

Statements:
1. No leopard is a cheetah: This statement implies that there is no overlap between the categories of leopards and cheetahs. In other words, there are no leopards that can be classified as cheetahs.

2. Some cheetahs are tigers: This statement suggests that there is a subset of cheetahs that can also be classified as tigers. It does not imply that all cheetahs are tigers, but it indicates that there is an overlap between these two categories.

3. All tigers are lions: This statement states that every tiger can be classified as a lion. It implies that there is no distinction between tigers and lions, and all tigers can be considered as lions.

Conclusions:
I. Some leopards are not tigers: This conclusion can be derived from the first statement, which states that there is no overlap between leopards and cheetahs. Since there are no leopards that are cheetahs and some cheetahs are tigers, it can be inferred that there are leopards that are not tigers.

II. All leopards are tigers: This conclusion cannot be logically derived from the given statements. The first statement clearly states that there is no overlap between leopards and cheetahs, and there is no information provided about the relationship between leopards and tigers. Therefore, it is not possible to conclude that all leopards are tigers.

Based on the above analysis:

- Conclusion I follows as it can be logically derived from the given statements.
- Conclusion II does not follow as there is no information provided to support this conclusion.

Therefore, the correct answer is option 'C' - if either conclusion I or II follows.

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