Logical Deduction :: Logic :: Type 2 (Three Premise Arguments)

• Logic - Type 1 (Two Premise Arguments)
• Logic - Type 2 (Three Premise Arguments)

In the following question, three statements are given followed by 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 with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements : No tree is fruit. All fruits are stones. All stones are rains.

Conclusions : I. No stone is tree. II. No rain is tree III. Some rains are fruits. IV. Some rains are trees.

Answer:

Explanation:

No tree is fruit. All fruits are stones.

Since the middle term 'fruits' is distributed twice, the conclusion must be particular. Since one premise is negative, the conclusion must be negative. So, it follows that 'Some stones are not trees'.

All fruits are stones. All stones are rains.

Clearly, it follows that 'All fruits are rains'. III is the converse of this conclusion and so it holds.

No tree is fruit. All fruits are rains.

As discussed above, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some rains are not trees'. However, II and IV involve only the extreme terms and form a complementary pair. Thus, either II or IV follows.

In the following question, three statements are given followed by 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 with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

 Statements : All doors are buses. All buses are leaves. No leaf is a flower. 

Conclusion : I. No flower is a door. II. No flower is a bus. III. Some leaves are doors. IV. Some leaves are buses.

Answer:

Explanation:

IV is the converse of the second premise and so it holds.

All doors are buses, All buses are leaves.

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 doors are leaves'. III is the converse of this conclusion and so it holds.

All buses are leaves. No leaf is a flower.

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 bus is flower'. II is the converse of this conclusion and so it holds.

All doors are buses. No bus is flower.

As discussed above, it follows that 'No door is flower', I is the converse of this conclusion and so it also holds.

In the following question, three statements are given followed by 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 with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

 Statements: Some tigers are lions. Some lions are rabbits. Some rabbits are horses. 

Conclusions : I. Some tigers are horses. II. Some rabbits are tigers. III. Some horses are lions. IV. All horses are rabbits.

Answer:

Explanation:

 Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn.

In the following question, three statements are given followed by 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 with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements: some bricks are trees. All trees are pens. All pens are boats. 

Conclusions: I. some boats are bricks II. some pens are bricks III. Some trees are bricks. IV. Some bricks are boats.

Answer:

Explanation:

 III is the converse of the first premise and so it holds.

Some bricks are trees. All trees are pens. 

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bricks are pens'. II is the converse of this conclusion and so it holds.

All trees are pens. All pens are boats.

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 trees are boats'.

Some bricks are trees. All trees are boats.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bricks are boats'. Thus, IV follows. I is the converse of this conclusion and so it also holds.

In the following question, three statements are given followed by 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 with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

 Statements: All rods are bricks. Some bricks are ropes. All ropes are doors.

conclusions: I. some rods are doors. II. some doors are bricks. III. Some rods are not doors. IV. All doors are ropes.

Answer:

Explanation:

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

• Logic - Type 1 (Two Premise Arguments)
• Logic - Type 2 (Three Premise Arguments)