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- Question
Statements:
All fruits are vegetables. All pens are vegetables. All vegetables are rains.
Conclusions:
- All fruits are rains.
- All pens are rains.
- Some rains are vegetables.
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
- Correct Answer
- All follow
ExplanationIII is the converse of the third premise and so it holds.All fruits are vegetables. All vegetables are rains.
The conclusion must be universal affirmative and should not contain the middle term.
So, it follows that 'All fruits are rains'. Thus, I follows.
All pens are vegetables. All vegetables are rains.
Clearly, it follows that 'All pens are rains'. Thus, II follows.
Logical Deduction problems
Search Results
- 1. Statements: Some taxis have horns. Some taxis have lights.
Conclusions:
- Every taxi has either horn or light.
- Some taxis have neither light nor horn.
- Some taxis have horns as well as lights.
- No taxi has horn as well as light.
Options- A. Only I and II follow
- B. Only II and III follow
- C. Only II and IV follow
- D. Either III or IV follows
- E. All follow Discuss
Correct Answer: Either III or IV follows
Explanation:
Since both the premises are particular, no definite conclusion follows. However, III and IV form a complementary pair. Thus, either III or IV follows.- 2. Statements: Some houses are offices. Some offices are schools.
Conclusions:
- Some schools are houses.
- Some offices are houses.
- No house is school.
- Some schools are offices.
Options- A. Only II and III follow
- B. Only I and IV follow
- C. Only either III or IV, and I follow
- D. Only II and IV and either I or III follow. Discuss
Correct Answer: Only II and IV and either I or III follow.
Explanation:
Since both the premises are particular, no definite conclusion follows. However, I and III involve only the extreme terms and form a complementary pair. So, either I or III follows. II is the converse of the first premise while IV is the converse of the second premise. Thus, both of them hold.- 3. Statements: Some bottles are drinks. All drinks are cups.
Conclusions:
- Some bottles are cups.
- Some cups are drinks.
- All drinks are bottles.
- All cups are drinks.
Options- A. Only I and II follow
- B. Only II and III follow
- C. Only II and IV follow
- D. Only III and IV follow
- E. Only I and IV follow Discuss
Correct Answer: Only I and II follow
Explanation:
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bottles are cups'. Thus, I follows. II is the converse of the second premise and so it also holds.- 4. Statements: Some books are pens. No pen is pencil.
Conclusions:
- Some pens are books.
- Some pencils are books.
- Some books are not pencils.
- All pencils are books.
Options- A. Only I follows
- B. Only II and III follow
- C. Only I and III follow
- D. Only I and II follow Discuss
Correct Answer: Only I and III follow
Explanation:
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. Thus, III follows. I is the converse of the first premise and so it also holds.- 5. Statements: All terrorists are guilty. All terrorists are criminals.
Conclusions:
- Either all criminals are guilty or all guilty are criminals.
- Some guilty persons are criminals.
- Generally criminals are guilty.
- Crime and guilt go together.
Options- A. Only I follows
- B. Only I and III follow
- C. Only II follows
- D. Only II and IV follow Discuss
Correct Answer: Only II follows
Explanation:
Since the middle term 'terrorists' is distributed twice in the premises, the conclusion cannot be universal. So, it follows that 'Some guilty persons are criminals'. Thus, II holds.- 6. Statements: Some towels are brushes. No brush is soap. All soaps are rats.
Conclusions:
- Some rats are brushes.
- No rat is brush.
- Some towels are soaps.
Options- A. None follows
- B. Only either I or II follows
- C. Only II follows
- D. Only I and III follow
- E. None of these Discuss
Correct Answer: Only either I or II follows
Explanation:
Some towels are brushes. No brush is soap.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 towels are not soaps'. No brush is soap. All soaps are rats.
Since the middle term is distributed twice, the conclusion must be particular. Since one premise is negative, the conclusion must be negative. So, it follows that 'Some brushes are not rats'. Since I and II involve the same terms and form a complementary pair, so either I or II follows.
- 7. 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.
- 8. 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.
- 9. 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.
- 10. 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.
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- 1. Statements: Some taxis have horns. Some taxis have lights.