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- Question
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
- Correct Answer
- Only either II or III follows
ExplanationSince 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.
Logical Deduction problems
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- 1. Statements: All trains are buses. No room is bus. All boats are rooms.
Conclusions:
- No boat is train.
- No bus is boat.
- No train is room.
Options- A. None follows
- B. Only I and II follow
- C. Only II and III follow
- D. Only I and III follow
- E. All follow Discuss
Correct Answer: All follow
Explanation:
All trains are buses. No room is bus.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 train is room'. Thus, III follows.
All boats are rooms. No room is bus.
As discussed above, it follows that 'No boat is bus'.
II is the converse of this conclusion and so it holds. All trains are buses. No boat is bus.
Again, it follows that 'No train is boat'. I is the converse of this conclusion and so it holds.
- 2. Statements: Some pens are books. All schools are books. Some colleges are schools.
Conclusions:
- Some colleges are pens.
- Some pens are schools.
- Some colleges are books.
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: None of these
Explanation:
Some pens are books. All schools are books.Since the middle term 'books' is not distributed even once in the premises, so no definite conclusion follows.
Some colleges are schools. All schools are books.
Since one premise is particular, the conclusion must be particular and should not contain the middle term.
So, it follows that 'Some colleges are books'. Thus, III follows.
Some pens are books. Some colleges are books.
Since both the premises are particular, no definite conclusion can be drawn.
Hence, only III follows.
- 3. Statements: Some saints are balls. All balls are bats. Some tigers are balls.
Conclusions:
- Some bats are tigers.
- Some saints are bats.
- All bats are balls.
Options- A. Only I and II follow
- B. Only II follows
- C. Only I and III follow
- D. Only III follows
- E. None of these. Discuss
Correct Answer: Only I and II follow
Explanation:
Some saints are balls. All balls are bats.Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some saints are bats'. Thus, II follows. Some tigers are balls. All balls are bats.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some tigers are bats'. I is the converse of this conclusion and so it holds.
- 4. Statements: Some hills are rivers. Some rivers are deserts. All deserts are roads.
Conclusions:
- Some roads are rivers.
- Some roads are hills.
- Some deserts are hills.
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 hills are rivers. Some rivers are deserts.Since both the premises are particular, no definite conclusion follows.
Some rivers are deserts. All deserts are roads.
Since one premise is particular, the conclusion must be particular and shouldn't contain the middle term. So, it follows that 'Some rivers are roads'. I is the converse of this conclusion and so it holds.
Some hills are rivers. Some rivers are roads.
Again, since both the premises are particular, no definite conclusion follows.
- 5. Statements: Some pictures are frames. Some frames are idols. All idols are curtains.
Conclusions:
- Some curtains are pictures.
- Some curtains are frames.
- Some idols are frames.
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 II and III follow
Explanation:
III is the converse of the second premise and so it holds.Some pictures are frames. Some frames are idols.
Since both the premises are particular, no definite conclusion follows.
Some frames are idols. All idols are curtains.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some frames are curtains'. III is the converse of this conclusion and so it holds.
Some pictures are frames. Some frames are curtains.
Since both the premises are particular, no definite conclusion can be drawn.
- 6. 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.- 7. 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.
- 8. 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.- 9. 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.
- 10. 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 Discuss
Correct Answer: None follows
Explanation:
All 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'.
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- 1. Statements: All trains are buses. No room is bus. All boats are rooms.