Logical Reasoning - Logical Problems - Discussion

(I) All drink mixes are beverages.

Thus, some beverages may or may not be drink mixes.

(II) all beverages are drinkable.

Thus some drinkable may not be beverages. It again means all drink mixes are drinkable since all beverages are drinkable.

(III) some beverages are red.

Thus, some may not be read. It again means that the beverages that are red may either be drink or non-drink mixes thus all may be drink mixes or all may be non-drink mixes or mixture of drink and non-drink mixes.

Conclusion:

From the facts and analysis, we can say that all that part of beverages that are red can be drink mixes and if it is drink mixes then it is drinkable since all beverages are drinkable and all drink mixes are beverages. Therefore "All red drink mixes are drinkable" is a fact.

Moreover, since all red drink mixes is a fact, then "Some drink mixes is red" because if some were not red then how did they became drinkable in the fact we have already proven? Thus if some were not, then we wouldn't have all red drink mixes been drinkable.

Therefore option C is the answer.

1. Statement I : "Some drink mixes are red."
- We know from Fact 3 that some **beverages" are red. However, there's no information in the facts that directly tells us that any **drink mixes** (a subset of beverages) are red. So, this statement "cannot be concluded as a fact".

2. Statement II: "All beverages are drink mixes."
- Fact 1 tells us that all drink mixes are beverages, but it doesn't imply that all beverages are drink mixes. There could be other beverages that are not drink mixes. So, this statement "is not a fact".

3. Statement III: "All red drink mixes are drinkable."
- Fact 2 tells us that all beverages are drinkable, and since all drink mixes are beverages (Fact 1), this would apply to red drink mixes as well. So, this statement "must be a fact".

Conclusion::
The correct answer is III only.

Here it is given that in fact 1 "all drink mixes are beverages", it does not mean that all the beverages will only be drink mixes, there might be some beverages which are not drink mixes. Hence Statement II is false.

In Fact 3 it is given that "some beverages are red", it does not mean that those beverages would be only drink mixes, it may or may not be. Hence it is uncertain. So Statement I is false.

In Fact 2 it is given that "all beverages are drinkable", it means all drink mixes which were beverages and beverages which wee red and beverages themselves it means everything is drinkable. Hence Statement III is true which means all drink mixes which may be red are drinkable. Hence only Statement III is true. It would be easily understood when we use Venn diagrams.

Drink mixes = beverages.
Beverages = drinkable.
Some beverages = red.

I) some drink mixes are red:

Ok, we know that all drink mixes are beverages but it is not explained that all beverages are drink mixes so this answer is not a known fact.

II) All beverages are drink mixes:

It is the same explanation than upper. We know that all drink mixes are beverages but it is not explained that all beverages are drink mixes so this answer is not a known fact.

III) All red drink mixes are drinkable:

For this one, we need to make the deduction. Indeed, we know that all drink mixes are beverages and that some beverages are red so some drink mixes are red and as all beverages = drink mixes = drinkable Finally all red drink mixes are drinkable which is a known fact.

Fact 1: All drink mixes are beverages : Here the mixes means for an eg we will take the mixes of fruit juice which is drinkable and called as beverages and could turn out to be any color.

Fact 2: All beverages are drinkable : So the mixes of juice are drinkable.

Fact 3: Some beverages are red : As we said it could turn out to be different color but some turn out to be red.

I: Some drink mixes are red : Yes agreed but it is uncertain.

II: All beverages are drink mixes : Not necessary.

III: All red drink mixes are drinkable : Yes it is drinkable thoe some may like some may not but it is drinkable.

Hope this may answer.

First you draw 3 concyclic circles innermost for drink mix, middle one for beverages and outer for drinkable.

1.1st option is wrong because lets take two more small circles one intersect all circle, and other intersecting only beverages and drinkable so by this diagram its clear that there are two cases for 1st option so it can not be a answer.

2. Second option is clearly wrong.

3. Third option is true because when you draw a circle intersecting drink mix i.e. is inner one it is always come under drinkable.

And most important don't mix 1, 2, 3 statement take it separately and try to find answer by this method.

Let's say drink mixes are cola. Since, all colas are beverages and all beverages are drinkable. But some beverages are red. Apple juice is also beverage. All colas and apple juices are beverages, and all beverages are drinkable.

But no cola is an apple juice so 1 is wrong. Not all beverage are cola, since apple juice is also a beverage, so 2 is wrong. All red drink mixes (a red cola or mirinda) are drinkable, hence 3 is right. So D is right. Best way to do it by drawing venn diagram, you would get a better understanding.

As per my opinion facts III is correct: As
Beverages are the subset of drinkable items.
Drink mixes are the subset of beverages.
Beverages may be red,orange, yellow, etc.
i.e. red beverages are the subset of beverages.

Statement 1: It may be true but not confirm because drink mixes are the subset of beverages and beverages may be red, orange, yellow, etc.

Statement 2: It is false because all drink mixes are beverages but all beverages may not be drink mixes.

Statement 3: It is true because all beverages are drinkable.

"All drink mixes are beverages" but not all beverages are drink mixes so we can conclude "some beverages are drink mixes" and "Some beverages are red".

I. Some drink mixes are red. - Only in extreme case it is true.

II. All beverages are drink mixes - Is false as per above discussion.

"All drink mixes are beverages" and "All beverages are drinkable". So we can say "All drink mixes are drinkable".

III. All red drink mixes are drinkable - true as cumulative result.

So Option D) III Only is the correct answer.

Statement 1 is wrong because all drink mixes are beverages but all beverages are not drink mixes.

Beverages constitutes of drink mixes and non drink mixes. So coming to the statement 'some drink mixes are red' and we know SOME beverages are red.

These SOME may constitute of:

1. Complete drink mixes.
2. Complete non drink mixes.
3. Both drink mixes and non drink mixes.

So any of the combination is possible. So it may be true or may not be. That's why it is considered FALSE.

Hope you get it. Thank you.