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 : Some dogs are rats. All rats are trees. Some trees are not dogs.

Conclusions : I. Some trees are dogs. II. All dogs are trees. III. All rats are dogs. IV. No tree is dog.

Answer:

Explanation:

Some dogs are rats. All rats are trees.

since one premise is particular, the conclusion must be particular and should not contain the middle term. so, it follows that'some dogs are trees', I is the converse of this conclusion and so it holds.

All rats are trees. Some trees are not dogs.

Since the middle term 'trees' is not distributed even once in the premises, 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 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 buildings are windows. No toys is building. Some tigers are toys. 

Conclusions: I. Some tigers are buildings. II. Some windows are tigers. III. All toys are tigers. IV. Some windows are toys.

Answer:

Explanation:

 No toy is building. All buildings are windows.

Since the middle term 'buildings' is distributed twice and one premise is negative, the conclusion must be particularly negative and should not contain the middle term. So, it follows that 'Some windows are not toys.

Some tigers are toys. No toy is building.

Since one premise is particular and the other premise is negative, the conclusion must be particularly negative and should not contain the middle term. So, it follows that 'Some tigers are not buildings'.

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 papers are cats. All cats are bats. No bat is horse.

Conclusions: I. Some papers are horses. II. No horse is cat. III. Some bats are papers. IV. All papers are bats.

Answer:

Explanation:

Some papers are cats. All cats are bats.

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

All cats are bats. No bat is horse.

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 cat is horse'. II is the converse of this conclusion and so it holds.

Some papers are bats. No bat is horse.

Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some papers are not horses'.

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 cups are glasses. Some glasses are bowls. No bowl is a plate.

Conclusions: I. No cup is a plate. II. No glass is a plate. III. Some plates are bowls. IV. Some cups are not glasses.

Answer:

Explanation:

All cups are glasses. Some glasses are bowls. 

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

Some glasses are bowls. No bowl is a plate.

Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some glasses are not plates'.

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 table is fruit. No fruit is window. All windows are chairs.

Conclusions : I. No window is table II. No chair is fruit III. No chair is table IV. All chairs are windows.

Answer:

Explanation:

No table is fruit. No fruit is window.

Since both the premises are negative, no definite conclusion follows.

No fruit is window. All windows are chairs.

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

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