NIELIT Scientific Assistant A 2020 November: 9

Question

Refer the statement and solve the question according to the conclusions.

$\text{Statement:}$

• $\text{Some Pigeons are Bird;}$
• $\text{Some Birds are Alive}$

$\text{Conclusion:}$

1. Some Pigeons are Alive
2. Some Birds are Pigeons

 

• A. Only (I) follows
• B. Only (II) follows
• C. Both (I) & (II) follows
• D. None follows

Answer 1

Given statements are: 

1. Some Pigeons are Bird.

 

2. Some Birds are Alive.

A conclusion “should always be true”. We can try to make the complement of the conclusion satisfiable (by drawing a Venn diagram) and if we can’t then the conclusion is VALID.

For the first conclusion “Some pigeons are alive” – the complement is “No pigeon is alive”. This is satisfiable as shown in the below Venn diagram obtained from the given statements. So, the given conclusion is not valid. 

For the second conclusion “Some birds are alive” – the complement is “No bird is alive”. This can’t be done in the Venn diagram satisfying the given two statements (hence not satisfiable). So, the given conclusion is valid.

Correct answer is $(C).$

Answer 2

We can solve this using the Venn diagram.

Consider the following diagram:

 conclusion (ii) “some birds are alive” is satisfying.

so option $B$ is correct here.

Comments

Actually for two statements you should use two different Venn diagrams. Then, should see in what all ways they can be combined and all valid conclusions can be determined. Your current Venn diagram gives many wrong conclusions like “No pigeon is alive”.

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 gatecse sir another possible way is as follows:

in this case, both conclusions are satisfied. Please verify it.

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Conclusion means “should always be true”. While drawing Venn diagram you try to make the complement of the conclusion satisfiable.

For first conclusion “Some pigeons are alive” – the complement is “No pigeon is alive” → this is what is shown in the given answer and that is correct and since the complement is satisfiable the given conclusion is not VALID. 

For second conclusion “Some birds are alive” – the complement is “No bird is alive” → this can’t be done in the Venn diagram satisfying the given two statements. That means the given conclusion is valid.

Your given answer is correct – just that the method is not clear.