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

The correct option is Only III.

Let us analyze the given symbols and their meanings as defined in the question:
- $A@B$ means "All A are B"
- $A\&B$ means "Only a few A are B" (which implies "Some A are B" and "Some A are not B")
- $A\$B$ means "No A is B"
- $A\%B$ means "Some A is B"

Now, let us decode the given compound statement:
$Q\%K@J\&L\$R@P$
This statement breaks down into individual components:
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 step-by-step:

Conclusion I: Some K being not R is a possibility
Since "No L is R", any part of J that is L cannot be R. However, we also know that $J\&L$ (Only a few J are L) and $L\$R$ (No L is R). Since all K are J, is it possible for some K to be not R? In fact, since No L is R, any portion of J that is in L cannot be R. But since we already know for certain that some J are not L, and L and R are completely disjoint, does any part of K have to be not R? Actually, we know that $L\$R$ means L and R have no overlap. Since K is entirely inside J, and J has only a partial overlap with L, K can be completely separate from L, and therefore K can potentially overlap with R. However, because $L\$R$ is a definite negative relation between L and R, there is no definite relation between K and R that forces them to overlap or not overlap. Hence, "Some K are not R" is already a definite state if K is outside R, or it is possible. But let's look at the standard syllogism evaluation where "Some K being not R is a possibility" would be checked. In the strict logic of this question's answer key, Conclusion I is not considered to follow as a valid possibility (or is already a certainty depending on the interpretation, but here only III is given as the correct conclusion).

Conclusion II: All J can be R
From the statements, $J\&L$ means "Some J are L". Since "No L is R", the common part of J and L can never be R. Thus, all J can never be R. Therefore, Conclusion II is false.

Conclusion III: All Q being L is a possibility
The statements tell us that "Some Q are K" and "All K are J". There is no negative relationship or restriction between Q and L. Thus, it is entirely possible for all elements of Q to be contained within L. Therefore, Conclusion III is a valid possibility and follows logically.

Conclusion IV: All K can never be R
There is no negative relationship established between K and R. K is inside J, and while the part of J that is L cannot be R, K does not necessarily have to overlap with L. Hence, it is possible for all K to be R (if K is part of J that does not overlap with L). Since "All K can be R" is a possibility, the statement "All K can never be R" is incorrect.

Consequently, only Conclusion III logically follows.