0 votes 0 votes 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. shivanisrivarshini asked Jul 28, 2016 shivanisrivarshini 1.9k points 4.7k views answer comment Share See all 0 reply Please log in or register to add a comment.
0 votes 0 votes both follows srestha answered Jul 28, 2016 srestha 5.2k points comment Share See all 20 Comments See all 20 20 Comments reply vijaycs 1.5k points commented Jul 28, 2016 reply Share @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 ? 2 votes 2 votes Arjun 8.6k points commented Jul 28, 2016 reply Share yes, it can be the case that there is no soldier outside the intersection. 1 votes 1 votes vijaycs 1.5k points commented Jul 28, 2016 reply Share yes sir , could not think of this point .. So, Sir what should be ans here - neither 1 nor 2. ?? 0 votes 0 votes shivanisrivarshini 1.9k points commented Jul 28, 2016 i edited by shivanisrivarshini Jul 28, 2016 reply Share 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 0 votes 0 votes vijaycs 1.5k points commented Jul 28, 2016 reply Share 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 ?? 0 votes 0 votes shivanisrivarshini 1.9k points commented Jul 28, 2016 reply Share 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 0 votes 0 votes vijaycs 1.5k points commented Jul 29, 2016 reply Share 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. 0 votes 0 votes shivanisrivarshini 1.9k points commented Jul 29, 2016 reply Share Yes u are right but how can u draw venn diagram for this 0 votes 0 votes vijaycs 1.5k points commented Jul 29, 2016 reply Share here more than one venn-diagram are possible because of word 'some'. 1 votes 1 votes shivanisrivarshini 1.9k points commented Jul 29, 2016 reply Share @vijay here neither 1 nor 2 , why not 1 ?? 0 votes 0 votes vijaycs 1.5k points commented Jul 29, 2016 reply Share see first two comments - one by @vijay and other by @arjun sir ,, and analyse the conclusion. 0 votes 0 votes shivanisrivarshini 1.9k points commented Jul 29, 2016 reply Share Fine got it thanks 1 votes 1 votes srestha 5.2k points commented Jul 29, 2016 reply Share 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 1 votes 1 votes vijaycs 1.5k points commented Jul 29, 2016 reply Share @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 0 votes 0 votes srestha 5.2k points commented Jul 29, 2016 reply Share 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. 0 votes 0 votes vijaycs 1.5k points commented Jul 29, 2016 reply Share 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. 0 votes 0 votes srestha 5.2k points commented Jul 30, 2016 reply Share @shivani what is the answer 0 votes 0 votes Arjun 8.6k points commented Jul 30, 2016 reply Share @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 1 votes 1 votes shivanisrivarshini 1.9k points commented Jul 30, 2016 reply Share Same as @vijay said neither 1 nor 2 1 votes 1 votes srestha 5.2k points commented Aug 10, 2016 reply Share 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? 0 votes 0 votes Please log in or register to add a comment.