Conclusions:
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.
Conclusions:
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'.
Conclusions:
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.
Conclusions:
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'.
Conclusions:
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.
Conclusions:
Conclusions:
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.
Conclusions:
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.
Conclusions:
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.
Conclusions:
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.
Conclusions:
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.
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