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: All benches are desks. Some desks are roads. All roads are pillars. 

Conclusions: I. some pillars are benches. II. some pillars are desks. III. Some roads are benches. IV. No pillar is bench.

Answer:

Explanation:

All benches are desks. Some desks are roads.

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

Some desks are roads. All roads are pillars.

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

All benches are desks. Some desks are pillars. 

Since the middle term 'desks' is not distributed even once in the premises, no definite conclusion follows. However, I and IV involve the extreme terms and form a complernentary pair. So, either I 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 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 needles are threads. All threads are boxes. All trees are boxes.

Conclusion: I. No needle is tree. II. Some trees are threads.  III. Some boxes are needles. IV. Some trees are needles.

Answer:

Explanation:

All needles are threads' All threads are boxes.

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 needles are boxes'. III is the converse of this conclusion and so it holds.

All threads are boxes. All trees are boxes.

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

All needles are boxes. All trees are boxes. 

Again, since the middle term 'boxes' is not distributed even once in the premises, no definite conclusion can be drawn. However, I and IV involve the extreme terms of these two statements and form a complementary pair. Thus, either I 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 pencils are birds. All birds are Skies. All skies are hills.

Conclusions: I. All pencils are hills . II. All hills are birds. III. All skies are pencils. IV. All birds are hills.

Answer:

Explanation:

All pencils are birds. All birds are skies.

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 Pencils are skies'.

All birds are skies. All skies are hills.

 As discussed above, it follows that 'All birds are hills'. Thu s, IV follows.

All pencils are skies. All skies are hills'.

Clearly, it follows that 'All pencils are hills'. Thus, I follows. Hence, I and IV follow.

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 uniforms are covers. All covers are papers. All papers are bags. 

Conclusions: I. All covers are bags.  II. Some bags are covers, papers and uniforms.  III. Some uniforms are not paper.

Answer:

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 follow. The converse of this conclusion i.e.' Some bags are covers' also hold.

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.

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 pictures are frames. Some frames are idols. All idols are curtains.

Conclusions: I. Some curtains are pictures. II. Some curtains are frames. III. Some idols are frames

Answer:

Explanation:

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.

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