statements and conclusions

Question

In each question below are two statements followed by two conclusions numbered I and II. You have to take the two given statements to be true even if they seem to be at variance from known facts and then decide which of the given conclusions logically commonly follows from the given statements disregarding commonly known facts.

Give answer(1) if only conclusion I follows.
Give answer(2) if only conclusion II follows.
Give answer (3) if either conclusion I or II follows.
Give answer (4) if neither conclusion I nor II follows.
Give answer (5) if both conclusions I and II follows.

1. Statements :
Some gears are wheels. All wheels are brakes.

Conclusions :
I. No brake is gear
II. Atleast some gears are brakes.

2. Statements :
No month is a year. No year is a second.

Conclusions :
I. All months are seconds.
II. No second is month.

3. Statements :
No plane is hill. Some hills are towns.

Conclusions :
I. No town is plane.
II. Some towns are plane.

4. Statements :
All metals are liquids. All liquids are gases.

Conclusions :
I. All metals are gases.
II. Atleast some gases are liquids.

5. Statements :
Some cities are towns. Some villages are cities.

Conclusions :
I. Atleast some villages are towns.
II. No village is a town

Answer 1

1. Statements :
Some gears are wheels. All wheels are brakes.

Conclusions :
I. No brake is gear
II. Atleast some gears are brakes.

Answer is 2 as some gears are wheels and hence since all wheels are brakes- those some must be brakes too. 

2. Statements :
No month is a year. No year is a second.

Conclusions :
I. All months are seconds.
II. No second is month.

Answer is 4 as neither can be derived from the given statements. 

3. Statements :
No plane is hill. Some hills are towns.

Conclusions :
I. No town is plane.
II. Some towns are plane.


Answer is 4 as neither can be derived from the given statements. 

4. Statements :
All metals are liquids. All liquids are gases.

Conclusions :
I. All metals are gases.
II. Atleast some gases are liquids.

Answer is 1 as all metals are liquids and all liquids are gases imply that all metals are gases. II need not be true as there can be a case that no liquids exist.  

5. Statements :
Some cities are towns. Some villages are cities.

Conclusions :
I. Atleast some villages are towns.
II. No village is a town

Answer is 4 as neither can be derived from the given statements. Some villages are cities and some cities are towns. But unless the "some" in both statements are the same, I needn't be true. 

Comments

For 3, I am getting the answer to be (2), i.e. only II follows.

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3. Statements :
No plane is hill. Some hills are towns.

Conclusions :
I. No town is plane.
II. Some towns are plane.

Here, No plane is hill. Some plane can be town. But there is no certainty -- it is just a possibility and hence cannot be taken as a conclusion. 

Answer 2

I need to draw venn diagram so how to reply here?

Comments

You can upload image