Logical Deduction — Part 2 MCQs with Explanations

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, only II follows.

Since one premise is particular and the other premise is negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some desks are not red'. However, I is the converse of the first premise and thus it holds.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, II follows. I is the converse of II and so it also holds.

Since the middle term 'divine' is not distributed even once in the premises, no definite conclusion can be drawn.

Since both the premises are universal and affirmative, the conclusion must be universal affirmative. However, conclusion II, being an A-type proposition, distributes the term 'cats'. Since the term 'cats' is distributed in II without being distributed in any of the premises, so conclusion II cannot follow. Thus, only I follows.

The subject in both the conclusions is vague. The true conclusion is 'No young scientist is superstitious'. Thus, neither I nor II follows,

Since one premise is particular, the conclusion must be particular and should not contain the middle term. Thus, it follows that 'Some pastries are chocolates', I is the converse of the second premise and so it holds. Since both the premises are affirmative, the conclusion cannot be negative. Thus, II does not follow.

Both the premises are A type propositions. So, the middle term 'honest' forming the predicate in each is not distributed in either. Since the middle term is not distributed even once, no definite conclusion follows.

Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All pens are houses'. II is the converse of this conclusion and so it holds. Since the term 'houses' is distributed in I without being distributed in any of the premises, so I does not follow.

Since the middle term 'smokers' is not distributed even once in the premises, no definite conclusion follows.

Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All branches are leaves'. Thus, I follows. IV is the converse of this conclusion and so it also holds.

Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, II follows. III is the converse of the first premise and thus it also holds.

Since the middle term 'trains' is not distributed even once in the/premises, no definite conclusion follows. However, III is the converse of the second premise while IV is the converse of the first premise. So, both of them hold.

Clearly, it follows that 'All politicians are fair'. I is the converse of the first premise, while III is the converse of the above conclusion. So, both I and III hold.

Since both the premises are particular, no definite conclusion follows. However, I and III involve only the extreme terms and form a complementary pair. Thus, either I or III follows.

Since both the premises are particular, no definite conclusion follows.

Since the middle term 'terrorists' is distributed twice in the premises, the conclusion cannot be universal. So, it follows that 'Some guilty persons are criminals'. Thus, II holds.

Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. Thus, III follows. I is the converse of the first premise and so it also holds.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bottles are cups'. Thus, I follows. II is the converse of the second premise and so it also holds.

Since both the premises are particular, no definite conclusion follows. However, I and III involve only the extreme terms and form a complementary pair. So, either I or III follows. II is the converse of the first premise while IV is the converse of the second premise. Thus, both of them hold.

Since both the premises are particular, no definite conclusion follows. However, III and IV form a complementary pair. Thus, either III or IV follows.

III is the converse of the third premise and so it holds. All fruits are vegetables. All vegetables are rains. The conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All fruits are rains'. Thus, I follows. All pens are vegetables. All vegetables are rains. Clearly, it follows that 'All pens are rains'. Thus, II follows.

Some towels are brushes. No brush is soap. 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 towels are not soaps'. No brush is soap. All soaps are rats. Since the middle term is distributed twice, the conclusion must be particular. Since one premise is negative, the conclusion must be negative. So, it follows that 'Some brushes are not rats'. Since I and II involve the same terms and form a complementary pair, so either I or II follows.

III is the converse of the second premise and so it holds. Some pictures are frames. Some frames are idols. Since both the premises are particular, no definite conclusion follows. Some frames are idols. All idols are curtains. Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some frames are curtains'. III is the converse of this conclusion and so it holds. Some pictures are frames. Some frames are curtains. Since both the premises are particular, no definite conclusion can be drawn.

Some hills are rivers. Some rivers are deserts. Since both the premises are particular, no definite conclusion follows. Some rivers are deserts. All deserts are roads. Since one premise is particular, the conclusion must be particular and shouldn't contain the middle term. So, it follows that 'Some rivers are roads'. I is the converse of this conclusion and so it holds. Some hills are rivers. Some rivers are roads. Again, since both the premises are particular, no definite conclusion follows.

Some saints are balls. All balls are bats. Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some saints are bats'. Thus, II follows. Some tigers are balls. All balls are bats. Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some tigers are bats'. I is the converse of this conclusion and so it holds.

Some pens are books. All schools are books. Since the middle term 'books' is not distributed even once in the premises, so no definite conclusion follows. Some colleges are schools. All schools are books. Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some colleges are books'. Thus, III follows. Some pens are books. Some colleges are books. Since both the premises are particular, no definite conclusion can be drawn. Hence, only III follows.

All trains are buses. No room is bus. 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 train is room'. Thus, III follows. All boats are rooms. No room is bus. As discussed above, it follows that 'No boat is bus'. II is the converse of this conclusion and so it holds. All trains are buses. No boat is bus. Again, it follows that 'No train is boat'. I is the converse of this conclusion and so it holds.

Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn. However, II and III are statements involving the extreme terms of the last two premises and form a complementary pair. Thus, either II or III follows.

Since each combination of premises has two particular premises, so no definite conclusion follows.

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.

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.

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 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'.

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.

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.

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.

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.

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 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.