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- Question
Statements: All tigers are lions. No cow is lion. Some camels are cows.
Conclusions:
- Some lions are camels.
- No camel- is tiger.
- Some tigers are cows.
Options- A. None follows
- B. Only I follows
- C. Only II follows
- D. Only III follows
- E. Either I or II follows
- Correct Answer
- None follows
ExplanationAll tigers are lions. No cow is lion.Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and shouldn't contain the middle term. So, it follows that 'No tiger is cow'.
Some camels are cows. No cow 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 camels are not lions'. Some camels are cows. No tiger 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 camels are not tigers'.
Logical Deduction problems
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- 1. Statements: All dolls are windows. All bottles are windows. All cars are bottles.
Conclusions:
- All cars are windows.
- Some cars are dolls.
- Some windows are cars.
Options- A. Only I and II follow
- B. Only II and III follow
- C. Only I and III follow
- D. All follow
- E. None of these Discuss
Correct Answer: Only I and III follow
Explanation:
All cars are bottles. All bottles are windows.Since both the premises are universal, the conclusion must be universal and shouldn't contain the middle term, So, it follows that 'All cars are windows'. Thus, I follows.
Also, III is the converse of this conclusion and so it holds.
All dolls are windows. All bottles are windows.
Since the middle term 'windows' is not distributed even once in the premises, no definite conclusion follows.
All cars are windows. All bottles are windows.
Again, the middle term 'windows' is not distributed even once in the premises.
So, no definite conclusion follows.
- 2. Statements: Some blankets are beds. Some pillows are blankets. All beds are pillows.
Conclusions:
- Some blankets are pillows.
- Some pillows are beds.
- Some beds are blankets.
Options- A. Only either I or II follows
- B. Only I and either II or III follow
- C. Only III and either I or II follow
- D. All I, II and III follow
- E. None of these Discuss
Correct Answer: All I, II and III follow
Explanation:
I is the converse of the second premise, II is the converse of the third premise and III is the converse of the first premise and as such, all three of them follow.- 3. Statements: Some boxes are hammers. Some hammers are beads. All beads are rings.
Conclusions:
- Some rings are hammers.
- Some hammers are boxes.
- Some rings are boxes.
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 and II follow
Explanation:
II is the converse of first premise and so it holds.Some boxes are hammers. Some hammers are beads.
Since both the premises are particular, no definite conclusion can be drawn.
Some hammers are beads. All beads are rings.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some hammers are rings'. I is the converse of this conclusion and so it holds.
Some boxes are hammers. Some hammers are rings.
Since both the premises are particular, no definite conclusion can be drawn.
- 4. Statements: Some blades are hammers. Some hammers are knives. Some knives are axes.
Conclusions:
- Some axes are hammers.
- Some knives are blades.
- Some axes are blades.
Options- A. None follows
- B. Only I follows
- C. Only II follows
- D. Only III follows
- E. None of these Discuss
Correct Answer: None follows
Explanation:
Since each combination of premises has two particular premises, so no definite conclusion follows.- 5. Statements: Some mountains are hillocks. Some mountains are rivers. Some mountains are valleys.
Conclusions:
- All mountains are either hillocks or rivers or valleys.
- No valley is river.
- Some river are valleys.
Options- A. None follows
- B. Only I follows
- C. Only either II or III follows
- D. Only III follows
- E. None of these Discuss
Correct Answer: Only either II or III follows
Explanation:
Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn. However, II and III are statements involving the extreme terms of the last two premises and form a complementary pair. Thus, either II or III follows.- 6. 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.
- 7. 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'.
- 8. 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.
- 9. 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.
- 10. 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.
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- 1. Statements: All dolls are windows. All bottles are windows. All cars are bottles.