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 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 towels are brushes. No brush is soap. All soaps are rats.

Conclusions : : I. Some rats are brushes. II. No rat is brush. III Some towels are soaps

Answer:

Explanation:

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.

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 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 tigers are lions. No cow is lion. Some camels are cows.

Conclusions: I. Some lions are camels. II. No camel is tiger. III. Some tigers are cows.

Answer:

Explanation:

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'.

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 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 hills are rivers. Some rivers are deserts. All deserts are roads

Conclusions: I. Some roads are rivers. II Some roads are hills. III. Some deserts are hills.

Answer:

Explanation:

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

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 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 fruits are vegetables. All pens are vegetables. All vegetables are rains.

Conclusions: I. All fruits are rains. II. All pens are rains. III. Some rains are vegetables.

Answer:

Explanation:

 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 follow.

All pens are vegetables. All vegetables are rains.

Clearly, it follows that 'All pens are rains'. Thus, II 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 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 dolls are windows. All bottles are windows. All cars are bottles.

Conclusions: I. All cars are windows. II. Some cars are dolls. III. Some windows are cars.

Answer:

Explanation:

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 follow.  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.

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