statements-conclusions

Question

Statements :1. Some soldiers are famous.
                   2. Some soldiers are intelligent.
 Conclusions:1.Some soldiers are either famous or intelligent.
                    2.Some soldiers are neither famous nor intelligent.

Answer 1

both follows

Comments

@srestha ... I think conclusion 2 is not true. Because we are not sure about soldier other than famous and intelligent.

when all soldiers are either famous or intelligent or both.

The above consideration follows the given statement but not the conclusion 2.

what do you say ?

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yes, it can be the case that there is no soldier outside the intersection.

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yes sir , could not think of this point ..

So, Sir what should be ans here - neither 1 nor 2.   ??

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By this we can say some soldiers are either famous or intelligent

and even some soldiers are neither famous nor intelligent

Even by this we can say both conclusions are true 

Please explain if i'm wrong

 

But Answwer is given as none 

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If we conclude any thing from some given statement then it(conclusion) should always be true in every condition. If we have any condition under the given statements that contradicts the conclusion then the conclusion should be false.

But here, for both the conclusion we have counter situation.

for 1st conclusion - think of when all the soldiers are famous and intelligent as well. In this condition either will give zero soldiers.

similarly, for 2nd conclusion - think of the situation as for 1st . Here also neither will result zero soldiers.

right ??

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In statements their are some soldiers are famous ---- this means thier are some soldiers even not famous

and some soldiers are intelligent ------- this means thier are some soldiers who are not intelligent

Conclusions contains some not all so both could be true na

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No @shivani ..

their are some soldiers are famous ---- this does not  mean there are some soldiers who are not famous.

and

        some soldiers are intelligent ------- this does not mean theer are some soldiers who are not intelligent.

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Yes u are right but how can u draw venn diagram for this

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here more than one venn-diagram are possible because of word 'some'.

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@vijay here neither 1 nor 2 , why not 1 ??

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see first two comments - one by @vijay and other by @arjun sir ,, and analyse the conclusion.

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Fine got it thanks

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but stmt 1 or stmt 2 , neither of them give any clue , that both of them represents total set.

the total set must be large than stmt1 and stmt2

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@srestha - word 'some'  can be treated as - at least one or not all or all.

see - https://www.google.co.in/search?q=some&oq=some&sourceid=chrome&ie=UTF-8

 

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then tell me difference between these three

1. Some soldiers are famous.

2. Some soldiers are intelligent.

 

1. All soldiers are famous.
 2. All of them are intelligent.

 

1. All soldiers are famous.
2. Some of them  are intelligent.

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see.  In first two sentence, the no of soldiers who are famous, are not certain . we can say  that - either some are not famous/intelligent or we can say all soldiers are famous/intelligent.

but in your 3rd and 4th sentence , All soldiers are famous/intelligent.

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@shivani what is the answer

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@srestha

Always consider a universal set.

Some people went to Delhi.

So, let the universe be the students in your class. (If the universe is not defined always consider the most general option). So, this means at least one student from class went to delhi. So, this implies:

$\exists x, G(x)$

and also

$\neg \forall x, \neg G(x)$ (which means it is not the case that no one had gone to Delhi)

Now,

Everyone went to Delhi.

This means every student in class went to Delhi which implies

$\neg \exists x, \neg G(x)$.

Now, the second case implies first. (This requires that the universe be non-empty, here it means at least one student in class and this assumption is usually used in many first order logic proofs)

http://math.stackexchange.com/questions/449418/why-does-the-semantics-of-first-order-logic-require-the-domain-to-be-non-empty

 

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Same as @vijay said neither 1 nor 2

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ok

Some people went to Delhi.

then only we ignore the case- no one had gone to Delhi

All other cases we have to consider.rt?