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 blankets are beds. Some pillows are blankets. All beds are pillows.

Conclusions: I. Some blankets are pillows. II. some pillows are beds. III. Some beds are blankets.

Answer:

Explanation:

I is the converse of the second premise, II is the converse of the third premise and III is the converse of the first premise and as such, all three of them 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 mountains are hillocks. some mountains are rivers. Some mountains are valleys.

Conclusions: I. All mountains are either hillocks or river or valleys. II. No valley is river.  III. Some river are valleys.

Answer:

Explanation:

Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn.However, II and III are statements involving the extreme terms of the last two premises and form a complementary pair. Thus, either II or III 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 trains are buses, No room is bus. All boats are rooms. 

Conclusions: I. No boat is train. II. No bus is boat. III. No train is room.

Answer:

Explanation:

All trains are buses. No room is bus.

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 train is room'. Thus, III follows.

All boats are rooms. No room is bus.

As discussed above, it follows that 'No boat is bus'.

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 flowers are toys. Some toys are trees. Some angels are trees.

Conclusions: I. Some angels are toys. II. Some trees are flowers III. Some flowers are angels.

Answer:

Explanation:

All flowers are toys. Some toys are trees.

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

Some toys are trees. Some angels are trees.

 Since both the premises are particular, 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 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 pens are books, All schools are books. some colleges are schools.

Conclusions: I. Some colleges are pens. II. Some pens are schools. III. Some colleges are books. 

Answer:

Explanation:

Some pens are books. All schools are books.

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

Some colleges are schools. All schools are books.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some colleges are books'. Thus, III follows.

Some pens are books. Some colleges are books.

Since both the premises are particular, no definite conclusion can be drawn. Hence, only III follows

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