Logical Reasoning - Logical Problems - Discussion

1) All Drink mixes are --->Beverages.

2) Other drinks can also be --->Beverages.

3) All Beverages (1 and 2) are ---->Drinkable.

4) Some beverages are Red.

Coming to the Statements:

I: Some drink mixes are red. ------- Need not be, other drinks can be red.

II: All beverages are drink mixes. ---- Need not be, Beverages can include other drinks as well.

III: All red drink mixes are drinkable. ---- YES since all beverages (which include drink mixes) are drinkable.

Every one here agrees that 3 is the right one. So lets not talk about it. The controversy here is about choice - one.

According to me,

If All Drink mixes are Beverages.

And Some beverages are red.

Possibility is - Yes some drink mixes can be red or may be not.

So since we are not sure if some drink mixes can be red, first choice can not be a fact (Actual Truth).

Even I got it wrong at the beginning then I understood.

Thank you.

I can't understand.

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.

It is specified that all drink mixes are beverages but it is not confirm that all the beverages are drink mixes. Hence only the 3rd statement is a fact.

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.

Use Venn diagrams.

Consider this example.

Drink mixes : Orange.

Beverages : Orange and Pomegranate.

Point 1:

All DM are B (so all orange are B).

Point 2:

All B are drinkable (so both orange and pomegranate are drinkable).

Point 3:

Some B are Red (so pomegranate are red).

Now Answer:

1. Some DM are Red = No in my example (can't say in general).

2. All B are DM = No, It say all DM are B nor B are DM.

3. All red DM are drinkable = Yes.

(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.

The name drink mixes indicates that it is drinkable. So, all red drink mixes are drinkable. All drink mixes are beverages. Some beverages (drink mixers) are red. Both I and III are correct.