Reasoning Aptitude > Logical Reasoning
LOGICAL DEDUCTION MCQs
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Answer: Option C. -> Only I and III follow
All cars are bottles. All bottles are windows.
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.
All cars are bottles. All bottles are windows.
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.
Answer: Option D. -> All I, II and III follow
I is the converse of the second premise, II is the converse of the third premise and III is the converse of the first premise and as such, all three of them follow.
I is the converse of the second premise, II is the converse of the third premise and III is the converse of the first premise and as such, all three of them follow.
Answer: Option C. -> Only I and II follow
II is the converse of first premise and so it holds.
Some boxes are hammers. Some hammers are beads.
Since both the premises are particular, no definite conclusion can be drawn.
Some hammers are beads. All beads are rings.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some hammers are rings'. I is the converse of this conclusion and so it holds.
Some boxes are hammers. Some hammers are rings.
Since both the premises are particular, no definite conclusion can be drawn.
II is the converse of first premise and so it holds.
Some boxes are hammers. Some hammers are beads.
Since both the premises are particular, no definite conclusion can be drawn.
Some hammers are beads. All beads are rings.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some hammers are rings'. I is the converse of this conclusion and so it holds.
Some boxes are hammers. Some hammers are rings.
Since both the premises are particular, no definite conclusion can be drawn.
Answer: Option E. -> None of these
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.
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.
Answer: Option B. -> Only I follows
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.
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.
Answer: Option B. -> Only I and II follow
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.
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.
Answer: Option D. -> Only either I or IV, and II follow
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.
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.
Answer: Option B. -> Only either I or III follows
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.
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.
Answer: Option E. -> None of these
All rods are bricks. Some bricks are ropes.
Since the middle term 'bricks' is not distributed even once in the premises, no definite conclusion follows.
Some bricks are ropes. All ropes are doors.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bricks are doors'. II is the converse of this conclusion and so it holds.
All rods are bricks. Some bricks are doors.
Since the middle term 'bricks' is not distributed even once in the premises, no definite conclusion follows.
However, I and III involve the extreme terms. But, since they are not contradictory, they do not form a complementary pair.
Hence, only II follows.
All rods are bricks. Some bricks are ropes.
Since the middle term 'bricks' is not distributed even once in the premises, no definite conclusion follows.
Some bricks are ropes. All ropes are doors.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bricks are doors'. II is the converse of this conclusion and so it holds.
All rods are bricks. Some bricks are doors.
Since the middle term 'bricks' is not distributed even once in the premises, no definite conclusion follows.
However, I and III involve the extreme terms. But, since they are not contradictory, they do not form a complementary pair.
Hence, only II follows.
Answer: Option B. -> Only either II or IV, and III follow
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.
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.
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