Logical Deduction - Study Mode
[#76] Statements : No rabbit is lion. Some horses are lions. All rabbits are tables. Conclusions : I. Some tables are lions. II. Some horses are rabbits. III. No lion is table.
Correct Answer
(B) Only either I or III follows
Explanation
Solution: 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.
[#77] 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.
Correct Answer
(D) Only either I or IV, and II follow
Explanation
Solution: 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.
[#78] 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.
Correct Answer
(B) Only I follows
Explanation
Solution: 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.
[#79] Statements : All doors are roads. No road is fruit. Some flowers are doors. Conclusions : I. Some fruits are doors. II. Some fruits are flowers. III. Some roads are flowers. IV. No fruit is flower.
Correct Answer
(B) Only either II or IV, and III follow
Explanation
Solution: All doors are roads. No road is fruit. 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 door is fruit. 'Some flowers are doors. All doors are roads. Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some flowers are roads'. Ill is the converse of this conclusion and so it holds. Some flowers are roads. No road is fruit. 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 flowers are not fruits'. II and IV involve the extreme terms and form a complementary pair. Thus, either II or IV follows.
[#80] Statements : All needles are threads. All threads are boxes. All trees are boxes. Conclusions : I. No needle is tree. II. Some trees are threads. III. Some boxes are needles. IV. Some trees are needles.
Correct Answer
None follows
Explanation
Solution: All needles are threads. All threads are boxes. 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 needles are boxes'. III is the converse of this conclusion and so it holds. All threads are boxes. All trees are boxes. Since the middle term 'boxes' is not distributed even once in the premises, no definite conclusion follows. All needles are boxes. All trees are boxes. Again, since the middle term 'boxes' is not distributed even once in the premises, no definite conclusion can be drawn. However, I and IV involve the extreme terms of these two statements and form a complementary pair. Thus, either I or IV follows.