Logical Reasoning - Logical Deduction

Exercise : Logical Deduction - Section 2
Directions to Solve

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

1.

Statements: All branches are flowers. All flowers are leaves.

Conclusions:

1. All branches are leaves.
2. All leaves are branches.
3. All flowers are branches.
4. Some leaves are branches.

None follows
Only I and IV follow
Only II and III follow
All follow
Explanation:
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.

2.

Statements: Some bags are pockets. No pocket is a pouch.

Conclusions:

1. No bag is a pouch.
2. Some bags are not pouches.
3. Some pockets are bags.
4. No pocket is a bag,

None follows
Only I and III follow
Only II and III follow
Only either I or IV follows
All follow
Explanation:
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.

3.

Statements: All aeroplanes are trains. Some trains are chairs.

Conclusions:

1. Some aeroplanes are chairs.
2. Some chairs are aeroplanes.
3. Some chairs are trains.
4. Some trains are aeroplanes.

None follows
Only I and II follow
Only II and III follow
Only III and IV follow
Explanation:
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.

4.

Statements: All politicians are honest. All honest are fair.

Conclusions:

1. Some honest are politicians.
2. No honest is politician.
3. Some fair are politicians.
4. All fair are politicians.

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

5.

Statements: Some clothes are marbles. Some marbles are bags.

Conclusions:

1. No cloth is a bag.
2. All marbles are bags.
3. Some bags are clothes.
4. No marble is a cloth.

Only either I or IV follows
Only either I or II follows
None follows
Only either I or III follows