Directions (30-32): In the following questions, the symbols- &, @, % and $ are used with the following meanings as illustrated below. In each of the questions given below statements are followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements regarding commonly known facts.

A@B means “ All A are B”
A&B means “Only a few A are B”
A$B means “No A is B”
A%B means “Some A is B”

Statement:

$Q\%K@\mathrm{J\&L}\$R@P$

Conclusions:

I.Some K being not R is a possibility

II.All J can be R

III.All Q being L is a possibility

IV.All K can never be R

Correct Answer: Both I and III

Let us decode the given symbols and their meanings first:
1. $A@B$ means "All A are B".
2. $A\&B$ means "Only a few A are B". This implies two conditions: "Some A are B" AND "Some A are not B".
3. $A\$B$ means "No A is B".
4. $A\%B$ means "Some A is B".

Now, let us decode the given combined statement step-by-step:
$Q\%K@J\&L\$R@P$
This can be broken down into individual statements:
1. $Q\%K$ ⇒ Some Q are K.
2. $K@J$ ⇒ All K are J.
3. $J\&L$ ⇒ Only a few J are L (meaning: Some J are L AND Some J are not L).
4. $L\$R$ ⇒ No L is R.
5. $R@P$ ⇒ All R are P.

Let us evaluate each conclusion based on these decoded statements:
Conclusion I: Some K being not R is a possibility
We know that No L is R. We are not given any definite negative relation between K and R that prevents them from overlapping or being completely disjoint. Since there is no definite relation that forces K to be entirely inside R, it is possible to draw K and R such that some part of K (or even all of K) is outside R. Hence, "Some K being not R is a possibility" is a valid scenario. Thus, Conclusion I follows.

Conclusion II: All J can be R
We know that "Only a few J are L", which means some part of J is always inside L (i.e., Some J are L). We also know that "No L is R". Therefore, the part of J that is inside L can never be R. Since a part of J can never enter R, it is impossible for All J to be R. Thus, Conclusion II does not follow.

Conclusion III: All Q being L is a possibility
The statements tell us that "Some Q are K", "All K are J", and "Only a few J are L". There is no direct negative restriction preventing Q from being entirely inside L. Since there is no statement that restricts Q from entering L completely, it is possible for All Q to be L. Thus, Conclusion III follows.

Conclusion IV: All K can never be R
To check if "All K can never be R" is true, we must see if it is impossible for All K to be R. We know that All K are J, and Only a few J are L, and No L is R. Since K is a subset of J, and only the portion of J that overlaps with L cannot be R, K (which is not necessarily inside L) can potentially be entirely within R without violating any conditions. Since it is possible for All K to be R, the statement "All K can never be R" (which means All K being R is impossible) is incorrect. Thus, Conclusion IV does not follow.

Therefore, only Conclusions I and III logically follow.