Logical Deduction - Section 4 (3)
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In each of the following questions, three statements are given followed by four conclusions numbered I, II, III and TV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
| 17. | Statements: Some spoons are bowls. All bowls are knives. All knives are forks. Conclusions: All spoons are forks. All bowls are forks. Some knives are bowls. Some forks are spoons. |
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Answer: Option E Explanation: III is the converse of the second premise and so it holds. Some spoons are bowls. All bowls are knives. Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some spoons are knives'. All bowls are knives. All knives are forks. 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 bowls are forks'. Thus, II follows. Some spoons are knives. All knives are forks. Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some spoons are forks'. IV is the converse of this conclusion and so it follows. Hence, II, III and IV follow. |
| 18. | Statements: Some tigers are lions. Some lions are rabbits. Some rabbits are horses. Conclusions: Some tigers are horses. Some rabbits are tigers. Some horses are lions. All horses are rabbits. |
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Answer: Option B Explanation: Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn. |
| 19. | Statements: All oceans are rivers. Some springs are rivers. All wells are springs. Conclusions: Some springs are oceans. Some wells are rivers. Some rivers are oceans. No well is river. |
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Answer: Option C Explanation: III is the converse of the first premise and so it holds. All oceans are rivers. Some springs are rivers. Since the middle term 'rivers' is not distributed even once in the premises, no definite conclusion follows. All wells are springs. Some springs are rivers. Since the middle term 'springs' is not distributed even once in the premises, no definite conclusion follows. However, II and IV involve the extreme terms and form a complementary pair. Thus, either II or IV follows. |
| 20. | Statements: All doors are buses. All buses are leaves. No leaf is a flower. Conclusions: No flower is a door. No flower is a bus. Some leaves are doors. Some leaves are buses. |
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Answer: Option E Explanation: IV is the converse of the second premise and so it holds. All doors are buses. All buses are leaves. 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 doors are leaves'. III is the converse of this conclusion and so it holds. All buses are leaves. No leaf is a flower. Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, it follows that 'No bus is flower'. II is the converse of this conclusion and so it holds. All doors are buses. No bus is flower. As discussed above, it follows that 'No door is flower'. I is the converse of this conclusion and so it also holds. |
| 21. | Statements: Some trains are roads. No road is jungle. All flowers are jungles. Conclusions: Some trains are flowers. Some trains are jungles. Some flowers are trains. No road is flower. |
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Answer: Option D Explanation: Some trains are roads. No road is jungle. 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 trains are not jungles'. No road is jungle. All flowers are jungles. Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, it follows that 'No flower is road'. IV is the converse of this conclusion and so it holds. Some trains are roads, No flower is road. As discussed above, it follows that 'Some trains are not flowers'. |
| 22. | 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. |
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Answer: Option A 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'. |
| 23. | 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. |
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Answer: Option D 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. |
| 24. | 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. |
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Answer: Option B 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. |