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- Question
Statements: Some uniforms are covers. All covers are papers. All papers are bags.
Conclusions:
- All covers are bags.
- Some bags are covers, papers and uniforms.
- Some uniforms are not papers.
Options- A. Only I follows
- B. Only I and II follow
- C. Only III follows
- D. All I, II and III follow
- E. None of these
- Correct Answer
- Only I and II follow
ExplanationSome uniforms are covers. All covers are papers.Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some uniforms are papers'. All covers are papers. All papers are bags.
Since both the premises are universal and affirmative, the conclusion must be universal affirmative (A-type) and should not contain the middle term. So, it follows that 'All covers are bags'. Thus, I follows. The converse of this conclusion i.e. 'Some bags are covers' also holds.
Some uniforms are covers. All covers are bags.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some uniforms are bags', The converse of this conclusion i.e. 'Some bags are uniforms' also holds.
Further, the converse of the third premise i.e. 'Some bags are papers' holds.
Now, II is the cumulative result of the conclusions 'Some bags are covers', 'Some bags are papers' and 'Some bags are uniforms'. Thus, II follows.
Logical Deduction problems
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- 1. Statements: All trees are flowers. No flower is fruit. All branches are fruits.
Conclusions:
- Some branches are trees.
- No fruit is tree.
- No tree is branch.
Options- A. None follows
- B. Only either I or III follows
- C. Only II follows
- D. Only either I or III, and II follow
- E. None of these Discuss
Correct Answer: None of these
Explanation:
All trees are flowers. No flower is fruit.Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term. So, it follows that 'No tree is fruit'. II is the converse of this conclusion and so it follows.
All branches are fruits. No flower is fruit.
Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term. So, it follows that 'No branch is flower'.
All trees are flowers. No branch is tree.
As discussed above, it follows that 'No tree is branch'. So, III follows.
Hence, both II and III follow.
- 2. Statements: All snakes are trees. Some trees are roads. All roads are mountains.
Conclusions:
- Some mountains are snakes.
- Some roads are snakes.
- Some mountains are trees.
Options- A. Only I follows
- B. Only II follows
- C. Only III follows
- D. Both I and II follow
- E. None follows Discuss
Correct Answer: Only III follows
Explanation:
All snakes are trees. Some trees are roads.Since the middle term is not distributed even once in the premises, so no definite conclusion follows.
Some trees are roads. All roads are mountains.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some trees are mountains'. III is the converse of this conclusion and so it holds.
All snakes are trees. Some trees are mountains.
Since the middle term is not distributed even once in the premises, so no definite conclusion follows.
- 3. Statements: All tigers are jungles. No jungle is bird. Some birds are rains.
Conclusions:
- No rain is jungle.
- Some rains are jungles.
- No bird is tiger.
Options- A. Only I and II follow
- B. Only III follows
- C. Only either I or II, and III follow
- D. All follow
- E. None of these Discuss
Correct Answer: Only either I or II, and III follow
Explanation:
All tigers are jungles. No jungle is bird.Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term.
So, it follows that 'No tiger is bird'. III is the converse of this conclusion and so it holds.
No jungle is bird. Some birds are rains.
Since one premise is particular and the other negative, the conclusion must be particular negative (O-type) and should not contain the middle term. So, it follows that 'Some jungles are not rains'.
Since I and II also involve the same terms and form a complementary pair, so either I or II follows.
- 4. Statements: Some rats are cats. Some cats are dogs. No dog is cow.
Conclusions:
- No cow is cat.
- No dog is rat.
- Some cats are rats.
Options- A. None follows
- B. Only I and II follow
- C. Only II and III follow
- D. Only III follows
- E. All I, II and III follow Discuss
Correct Answer: Only III follows
Explanation:
III is the converse of the first premise and so it holds.Some rats are cats. Some cats are dogs.
Since both the premises are particular, no definite conclusion follows.
Some cats are dogs. No dog is cow.
Since one premise is particular and the other negative, the conclusion must be particular negative (O-type) and should not contain the middle term. So, it follows that 'Some cats are not cows'.
- 5. Statements: All flowers are toys. Some toys are trees. Some angels are trees.
Conclusions:
- Some angels are toys.
- Some trees are flowers.
- Some flowers are angels.
Options- A. None follows
- B. Only I follows
- C. Only II follows
- D. Only III follows
- E. Only I and III follow Discuss
Correct Answer: None follows
Explanation:
All flowers are toys. Some toys are trees.Since the middle term 'toys' is not distributed even once in the premises, no definite conclusion follows.
Some toys are trees. Some angels are trees.
Since both the premises are particular, no definite conclusion can be drawn.
- 6. Statements: No rabbit is lion. Some horses are lions. All rabbits are tables.
Conclusions:
- Some tables are lions.
- Some horses are rabbits.
- No lion is table.
Options- A. None follows
- B. Only either I or III follows
- C. Only II and III follow
- D. Only III follows
- E. None of these Discuss
Correct Answer: Only either I or III follows
Explanation:
Some horses are lions. No rabbit is lion.Since one premise is particular and the other negative, the conclusion must be particular negative (O-type) and should not contain the middle term.
So, it follows that 'Some horses are not rabbits'.
All rabbits are tables. No rabbit is lion.
Since the middle term 'rabbits' is distributed twice, the conclusion must be particular.
Since one premise is negative, the conclusion must be negative. So, it follows that 'Some tables are not lions'. Since I and III involve the same terms and form a complementary pair, so either I or III follows.
- 7. Statements: All benches are desks. Some desks are roads. All roads are pillars.
Conclusions:
- Some pillars are benches.
- Some pillars are desks.
- Some roads are benches.
- No pillar is bench.
Options- A. None follows
- B. Only either I or IV, and III follow
- C. Only either I or IV follows
- D. Only either I or IV, and II follow
- E. All follow Discuss
Correct Answer: Only either I or IV, and II follow
Explanation:
All benches are desks. Some desks are roads.Since the middle term 'desks' is not distributed even once in the premises, no definite conclusion follows.
Some desks are roads. All roads are pillars.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some desks are pillars'. II is the converse of this conclusion and so it holds.
All benches are desks. Some desks are pillars.
Since the middle term 'desks' is not distributed even once in the premises, no definite conclusion follows. However, I and IV involve the extreme terms and form a complementary pair. So, either I or IV follows.
- 8. Statements: Some dogs are rats. All rats are trees. Some trees are not dogs.
Conclusions:
- Some trees are dogs.
- All dogs are trees.
- All rats are dogs.
- No tree is dog.
Options- A. None follows
- B. Only I follows
- C. Only I and II follow
- D. Only II and III follow
- E. All follow Discuss
Correct Answer: Only I follows
Explanation:
Some dogs are rats. All rats are trees.Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some dogs are trees'. I is the converse of this conclusion and so it holds.
All rats are trees. Some trees are not dogs.
Since the middle term 'trees' is not distributed even once in the premises, no definite conclusion follows.
- 9. Statements: Some bricks are trees. All trees are pens. All pens are boats.
Conclusions:
- Some boats are bricks.
- Some pens are bricks.
- Some trees are bricks.
- Some bricks are boats.
Options- A. Only I and II follow
- B. Only III and IV follow
- C. None follows
- D. All follow
- E. None of these Discuss
Correct Answer: All follow
Explanation:
III is the converse of the first premise and so it holds.Some bricks are trees. All trees are pens.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bricks are pens'. II is the converse of this conclusion and so it holds.
All trees are pens. All pens are boats.
Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All trees are boats'.
Some bricks are trees. All trees are boats.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bricks are boats'. Thus, IV follows. I is the converse of this conclusion and so it also holds.
- 10. Statements: All cups are glasses. Some glasses are bowls. No bowl is a plate.
Conclusions:
- No cup is a plate.
- No glass is a plate.
- Some plates are bowls.
- Some cups are not glasses.
Options- A. None follows
- B. Only either I or III follows
- C. Only II and III follow
- D. Only III and IV follow
- E. None of these Discuss
Correct Answer: None follows
Explanation:
All cups are glasses. Some glasses are bowls.Since the middle term 'glasses' is not distributed even once in the premises, no definite conclusion follows.
Some glasses are bowls. No bowl is a plate.
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some glasses are not plates'.
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- 1. Statements: All trees are flowers. No flower is fruit. All branches are fruits.