statements: Some uniforms are covers. All covers are papers. All papers are bags. Conclusions: I.All covers are bags. II.Some bags are covers, papers and uniforms. III.Some uniforms are not papers.
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.
statements: All trees are flowers. No flower is fruit. All branches are fruits.Conclusions: I.Some branches are trees.II.No fruit is tree.III.No tree is branch.
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.
statements: All snakes are trees. Some trees are roads. All roads are mountains. Conclusions: I.Some mountains are snakes. II.Some roads are snakes. III.Some mountains are trees.
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.
statements: All benches are desks. Some desks are roads. All roads are pillars. Conclusions: I.Some pillars are benches. II.Some pillars are desks. III.Some roads are benches. IV.No pillar is bench.
All benches are desks. Some desks are roads.
Since the middle term 'desks' is not distributed even once in the premises, no definite conclusion follows.
Some desks are roads. All roads are pillars.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some desks are pillars'. II is the converse of this conclusion and so it holds.
All benches are desks. Some desks are pillars.
Since the middle term 'desks' is not distributed even once in the premises, no definite conclusion follows. However, I and IV involve the extreme terms and form a complementary pair. So, either I or IV follows.
statements: Some dogs are rats. All rats are trees. Some trees are not dogs. Conclusions: I.Some trees are dogs. II.All dogs are trees. III.All rats are dogs. IV.No tree is dog.
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.
statements: All cups are glasses. Some glasses are bowls. No bowl is a plate. Conclusions: I.No cup is a plate. II.No glass is a plate. III.Some plates are bowls. IV.Some cups are not glasses.
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'.
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