# Logical Reasoning - Logical Deduction

Exercise : Logical Deduction - Section 3
Directions to Solve

In each of the questions below are given three statements followed by three conclusions numbered I, II and III, You have to take the given statements to be true even if they seem to be at variance from the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

16.

Statements: All tigers are jungles. No jungle is bird. Some birds are rains.

Conclusions:

1. No rain is jungle.
2. Some rains are jungles.
3. No bird is tiger.

Only I and II follow
Only III follows
Only either I or II, and III follow
All follow
None of these
Explanation:

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.

17.

Statements: All snakes are trees. Some trees are roads. All roads are mountains.

Conclusions:

1. Some mountains are snakes.
2. Some roads are snakes.
3. Some mountains are trees.

Only I follows
Only II follows
Only III follows
Both I and II follow
None follows
Explanation:

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.

18.

Statements: All trees are flowers. No flower is fruit. All branches are fruits.

Conclusions:

1. Some branches are trees.
2. No fruit is tree.
3. No tree is branch.

None follows
Only either I or III follows
Only II follows
Only either I or III, and II follow
None of these
Explanation:

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.

19.

Statements: Some uniforms are covers. All covers are papers. All papers are bags.

Conclusions:

1. All covers are bags.
2. Some bags are covers, papers and uniforms.
3. Some uniforms are not papers.

Only I follows
Only I and II follow
Only III follows
All I, II and III follow
None of these
Explanation:

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.

20.

Statements: No rabbit is lion. Some horses are lions. All rabbits are tables.

Conclusions:

1. Some tables are lions.
2. Some horses are rabbits.
3. No lion is table.

None follows
Only either I or III follows
Only II and III follow
Only III follows
None of these