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Assume that each one of the numbered statements are individually true. Each of the two choices consists of a subset of these statements. Choose the subset as your answer where the statements therein are logically consistent among themselves.

  1. Mangoes are not oranges.
  2. Grapes are apples.
  3. Apples are mangoes.
  4. Mangoes are bananas.
  5. Bananas are oranges.
  6. Oranges are grapes.
  7. Bananas are not apples.

Options: (A) 2, 3, 4, 5, 6; (B) 1, 4, 2, 6, 7

Answer:

Option (B)

Why is the other option not the correct answer?

Note: I had asked similar question in Logical Connection Problems: which sets of statements are logically consistent? also but since SQLnoob had cleared major part of the doubt there so question was quite redundant and to be fair to SQLnoob, I did not edit my question. Only doubt mentioned here remains. It wasn't coming into the limelight on the other post.

Edit: I've got the general idea that many people here think that option A is consistent and the answer given saying only option B is incorrect.

I can't delete this question as I have an answer already and neither can I edit this post further as then it won't be solving it's purpose (of doubt clearance) so kindly refrain from further downvoting the post and if anyone has different opinion from the general idea, please leave an answer or a comment, I'll be glad to engage.

If you have a differing opinion, you might be interested in hearing one such opinion that I didn't get how it works though:

In option (A) all statements are affirmative and universal statements, where each term is mentioned exactly twice but distributed exactly once. So, they are not consistent.

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  • $\begingroup$ Does this answer your question? Logical Connection Problems: which sets of statements are logically consistent? $\endgroup$
    – Auribouros
    Jun 10 at 11:36
  • $\begingroup$ @Auribouros please read my question till the end. $\endgroup$ Jun 10 at 11:38
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    $\begingroup$ As pointed out elsewhere, I think your questions are either missing a lot of source-specific context, or are just from a bad source. We're not really going to be able to make sense of whatever nonstandard logic the text is using that would indicate, for example, that A is not a correct answer for question 1. $\endgroup$
    – SQLnoob
    Jun 10 at 13:15
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    $\begingroup$ All seven of these statements are logically consistent, with the conclusion that no instances of these five fruit types exist. $\endgroup$
    – Magma
    Jun 10 at 15:31
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    $\begingroup$ The only bit of sense I can get from this is that in set A none of the statements can be deduced from the others. But in set B statement 1 can be deduced from the others. But, well, that is not what I call logical consistency. $\endgroup$
    – Florian F
    Jun 11 at 17:18

1 Answer 1

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[EDITED to add:] Since I posted this InanimateBeing has edited the question in a way that makes parts of it no longer make much sense. What's now in InanimateBeing's question is what was originally Q2, and there was originally also a "hint" for that question that had allegedly been supplied and which InanimateBeing was asking about.

I think the meaning of the questions is rather unclear, and whether option A in Q1 is an acceptable answer depends on interpretation.

Option A (2,3,4,5,6) gives us a circular chain like this: As are Bs, Bs are Cs, Cs are Ds, Ds are Es, Es are As. These are obviously all consistent with one another if we allow everything to be the same (so e.g. all those fruit names are just code for some single type of thing), and they are not consistent if we assume that different words have to denote different sets of things.

The fact that the question doesn't make this clearer is a deficiency in the question.

The hint for Q2 is just incorrect. If I say e.g. "Xs are not Ps", "Ys are not Qs" and "Zs are not Rs" then I have made an odd number of negative statements but they are clearly consistent with one another. Likewise if I say "Some As are not Bs", "Some Bs are not Cs", and "Some Cs are not Ds".

There isn't even an inconsistency when you have a cycle like this: "Some As are not Bs", "Some Bs are not Cs", "Some Cs are not As". (Imagine that A,B,C denote disjoint sets of things: actual literal apples, oranges and grapes, for instance.) The same applies if we have "No As are Bs", "No Bs are Cs", and "No Cs are As".

And in fact option A in Q2, which they say is inconsistent, is perfectly consistent (so long as we ignore the actual meanings of the words they are using). Suppose there are 6 things. 1 is red and green. 2 is orange. 3 is green. 4 is blue. 5 is violet. 6 is orange and violet. Then: "Some violets are not blue" is true (5 and 6 are both violet-but-not-blue). "No orange is red" is true (2 is the only orange thing and it isn't red). "Some oranges are violets" is true (6 is orange and is also violet). "Every red is green" is true (1 is the only red thing, and it is also green). "No green is blue" is true (1 and 3 are the only green things, and they are not blue).

I think that whoever wrote the things you're using was incompetent and you should not be taking their advice.

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  • $\begingroup$ would you agree with this that had there been only 1 negative statement in among the 5 statements then no conclusion can be drawn? $\endgroup$ Jun 10 at 11:29
  • $\begingroup$ If one statement were "some apples are oranges" and another were "no apples are oranges" then there would be a contradiction from just those, so no. $\endgroup$
    – Gareth McCaughan
    Jun 10 at 17:56
  • $\begingroup$ The reason one negative statement doesn't works is that since all other are positive statements so we can't end up with a negative statement with respect to circular logic and similarly, using a negative statement can never lead us to a positive conclusion in same regards (circular logic). $\endgroup$ Jun 10 at 18:15
  • $\begingroup$ My apologies for the inconvenience caused $\endgroup$ Jun 10 at 18:31

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