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 fruits are flowers. No flower is a boat. All boats are rivers.

Conclusions: I. some fruits are rivers.   

                   II. some rivers are boats

                   III. Some rivers are fruits.

                   IV. Some flowers are fruits.

Answer:

Explanation:

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

II is the converse of the third premise and so it holds.

Some fruits are flowers. No flower is a boat.

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

No flower is a boat. All boats are rivers.

Since the middle term is distributed twice, the conclusion cannot be universal. Again since one premise is negative, the conclusion must be negative and shouldn't contain the middle term. So, it follows that 'Some flowers are not rivers' Thus, only II and IV follow. Hence, the answer is (c)

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 rains. All papers are buildings. All dogs are paper.

Conclusions: I. All dogs are rain. 

                   II.   Some papers are rains.

                   III. Some rains are in buildings.

                   IV.  Some rains are paper.

Answer:

Explanation:

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

All papers are buildings. All buildings are rains.

Since both the premises are universal and affirmative, the conclusion must also be universal and affirmative and should not contain the middle term. So, it follows that 'All papers are rains'. IV is the converse of this conclusion and so it holds.

Clearly, it follows that 'All dogs are buildings'.

All dogs are buildings. All buildings are rains.

Clearly, it follows that 'All dogs are rains', So, I follows. Thus, I, III and IV follow from the given premises. Hence, the answer is (e)

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