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:

$C\$E\%G@B\&D$

Conclusions:

I. All B being D is a possibility

II. Some B being C is not a possibility

III. All G can never be C

IV. All D can be E

The correct option is Both III and IV.

Let us decode the symbols used in the statements according to the given rules:
1. $A@B$ means "All A are B"
2. $A\&B$ means "Only a few A are B" (which implies: 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 combined statement:
Statement: $C\$E\%G@B\&D$
Breaking it down:
- $C\$E$ ⇒ No C is E.
- $E\%G$ ⇒ Some E is G.
- $G@B$ ⇒ All G are B.
- $B\&D$ ⇒ Only a few B are D (meaning: Some B are D, and Some B are not D).

Let us analyze each conclusion based on these statements:

Conclusion I: All B being D is a possibility.
From the statement, we have $B\&D$, which means "Only a few B are D". This statement explicitly implies that "Some B are not D" is definitely true. Since we know for certain that some part of B can never be D, it is impossible for all B to be D. Therefore, Conclusion I does not follow.

Conclusion II: Some B being C is not a possibility.
This can be rephrased as: "It is impossible that some B are C" or "No B can ever be C". Let us check if some B can be C. The only constraint on C is that no C is E. Part of B contains G, and G contains a part of E. But the remaining parts of B that do not overlap with E are free to overlap with C. Therefore, "Some B being C" is a valid possibility. Since it is possible, saying "Some B being C is not a possibility" is false. Thus, Conclusion II does not follow.

Conclusion III: All G can never be C.
From the statements, we know that "Some E is G" (or some G is E) and "No C is E" (which means no E can be C). Since the part of G that overlaps with E can never be C, it is impossible for all of G to be C. Thus, All G can never be C is a true and definite conclusion. Therefore, Conclusion III follows.

Conclusion IV: All D can be E.
We have the relation $B\&D$ (Only a few B are D), which tells us that some B are not D, and some B are D. There is no restriction preventing all elements of D from being inside E. Since there is no negative constraint between D and E, it is possible for all D to be E. Therefore, Conclusion IV follows.

Thus, only conclusions III and IV follow.