# Logical Connection Problems: which sets of statements are logically consistent? [closed]

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

Q1:

1. Those who think more can create new things.
2. Those who do not have brain are dull.
3. Those who have a brain are intelligent people.
4. Those who have a brain are artists.
5. Some intelligent people are not artists.
6. Intelligent people think more.
7. Dull people cannot think more.
8. Those who can create new things are artists.

Options:

1. 1, 4, 3, 8 and 6
2. 8, 5, 6, 1 and 3
3. 2, 7, 6, 5 and 4
4. 2, 3, 4, 6 and 1

Q2:

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.
8. No mango is an orange.

Options:

1. 2, 3, 4, 5 and 6
2. 1, 4, 2, 6 and 7
3. 3, 4, 5, 6 and 7
4. 8, 4, 6, 2 and 3

Q3:

1. Some violets are not blue.
2. All oranges are red.
3. No orange is red.
4. Some oranges are violets.
5. Some blues are greens.
6. Every red is green.
7. No green is blue.
8. All violets are red.

Options:

1. 1, 2, 6, 5 and 4
2. 1, 3, 4, 6 and 7
3. 1, 2, 7, 6 and 4
4. 2, 8, 6, 5 and 7

I'm generally able to solve these types of questions when there are only 3 statements, but I don't know how to solve the above questions. I found these questions in one of the booklets on logical reasoning that I have recently started practicing from. In each of the questions, the answer comes out by a different approach so asking only 1 of them wouldn't have solved my problem.

How would one solve the above 3 questions?

Here's my attempt at Q2 (Tick means distributed and cross means undistributed):

1. $$G\checkmark A\times$$; $$A\checkmark M\times$$; $$M\checkmark B\times$$; $$B\checkmark O\times$$; $$O\checkmark G\times$$;

2. $$M\checkmark O\checkmark$$; $$M\checkmark B\times$$; $$G\checkmark A\times$$; $$O\checkmark G\times$$; $$B\checkmark A\checkmark$$;

3. $$A\checkmark M\times$$; $$M\checkmark B\times$$; $$B\checkmark O\times$$; $$O\checkmark G\times$$; $$B\checkmark N\checkmark$$;

4. $$M\checkmark O\checkmark$$; $$M\checkmark B\times$$; $$O\checkmark G\times$$; $$G\checkmark A\times$$; $$A\checkmark M\times$$;

But beyond this I couldn't move a step ahead in figuring out which one out of the 4 is correct.

Hint:

Odd number of negative or particular statements by default make that option invalid.

I would love to know the reasoning behind the hint too.

Answers to the questions are as follows:

Q1:

Option 1

Q2:

Option 2

Q3:

Option 3

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Jun 8 at 11:49
• May I know the reason for down vote please, would help me and the community when I ask questions in future? Jun 8 at 14:53
• The downvote probably came because this is too much like a "help me with my homework" question. It may have helped if you put your request for help at the top so that it's the first thing readers see - the downvoter may not have seen that before downvoting and leaving. Also, you need to include attribution for these puzzles (at minimum, the name of booklet you got them from). Jun 8 at 17:57
• I am not sure what makes sentences "logically consistent". A sentence like "mangoes are not oranges" says there are no fruits that are both mangoes and oranges. Similarily the sentences "bananas are apples" and "bananas are not apples" say that there are no bananas that are not apples resp. that there are no bananas that are apples. It is not inconsistent. It only says there are no bananas. Jun 9 at 3:31
• @InanimateBeing "All bananas are apples" and "no bananas are apples" are both true if there are no bananas. Jun 9 at 6:39

For Q1:

Option 1 works. Those who have brain are intelligent [3], therefore they think more [6], therefore they can create new things [1], therefore they are artists [8]. This is consistent with the conclusion of [4].

Option 2 is not correct. Intelligent people think more [6], therefore they can create new things [1], therefore they are artists [8]. This contradicts [5].

Option 3 is not correct. People with brain are artists [4], and people without brain are dull [2]. An intelligent person cannot be dull [6, 7], therefore they must have brain and therefore be artists, but this contradicts [5].

I don't see a logical contradiction within the statements of option 4, but it also doesn't lend itself as neatly to a conclusion like option 1 does, so I'm guessing option 1 is the intended answer?

For Q2:

Option 3 doesn't work. Apples are mangoes [3], therefore they are bananas [4]. This contradicts [7].

Option 4 doesn't work. Oranges are grapes [6], therefore they are apples [2], therefore they are mangoes [3]. This contradicts [8].

Like Q1, there's not contradiction with option 2, but it doesn't lead to a nice circular conclusion like option 1 does, so I'm guessing option 1 is the intended answer. Grapes are apples [2], therefore mangoes [3], therefore bananas [4], therefore oranges [5]. This is consistent with the conclusion of [6].

For Q3:

Option 4 doesn't work, because [e] and [g] are contradictory. At a glance, the rest don't seem to have any obvious contradictions. Not sure what the intention is here.

• thank you trying this tedious problem. Your answer to only Q1 is correct. I'm putting the answers in my question can you edit and hide them in "reveal spoiler" form? Jun 8 at 13:45
• When you say "yes" I'll put the answers there Jun 8 at 13:45
• If you know the answers and are just looking for an explanation of why they're correct, just add them to your question. You can hide them in spoilers, like a hint. Jun 8 at 14:07
• You'll need to provide attribution for where you found these questions and why you believe the answers are what they say they are. For example, in Q2 there is nothing inconsistent with option 1 (in fact option 1 seems like the obviously correct answer), so it's unclear how or why the correct answer would be option 2. It feels like the puzzle is missing some context. Jun 8 at 14:41
• I was just reading your answers again, and noted a very important thing that you had mentioned in your answers, that is, "but it doesn't lead to a nice circular conclusion". I didn't know I need to check for circular conclusion. This is a great help as I was clueless how to even approach the question. It would be great if you start your answer with statements like: "In this question you need to look for circular conclusion" and then give the answers so that it gets highlighted. Jun 8 at 15:29

I'd suggest finding a different resource to help you practice logical reasoning. It's possible that the booklet's definition of "logically consistent" does allow for the given problems to have the stated correct answers, but that definition is different enough from what is actually logically consistent that using it for learning will be more harmful than helpful.

First let's take a look at the hint - having an odd number of negative statements by default makes an option invalid. This is not something that actually affects logical consistency. For example, consider the following five statements:

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

This is perfectly logically consistent - it is the real world scenario.

Outside of the context of this booklet, something being "logically consistent" means that it does not have any inherent contradictions. As @SQLnoob's answer points out, some of the options for these questions are definitely not logically consistent - following the chains of reasoning leads to contradictions. However, some of the "wrong" answers do not lead to any contradictions, so they are logically consistent even though the booklet claims they are not.

• this questions comes under "Logical Connectives" and it is well-known that if all the statements are negative or/and particular then no conclusion can be drawn. Jun 9 at 17:49
• Also, SQLnoob has cleared majority of my doubts so my question stands redundant, but if I reduce my question length then it would do injustice to SQLnoob's answer so what should I do? Jun 9 at 17:50