Logical Deduction - Section 3
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In each of the questions below are given three statements followed by three conclusions numbered I, II and III, You have to take the given statements to be true even if they seem to be at variance from the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
| 1. | 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. |
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Answer: Option B 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. |
| 2. | 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. |
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Answer: Option B Explanation: Some 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. |
| 3. | 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. |
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Answer: Option E 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. |
| 4. | 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. |
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Answer: Option C 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. |
| 5. | 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. |
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Answer: Option C 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. |
| 6. | 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. |
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Answer: Option D 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'. |
| 7. | 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. |
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Answer: Option A 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. |
| 8. | 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. |
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Answer: Option A 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'. |