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 answer is Both III and IV.

Let us decode the given symbols based on the instructions:
1. $A@B$ means "All A are B".
2. $A\&B$ means "Only a few A are B" (which implies both "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".

Step 1: Breakdown of the Statement
The given statement is:
$C\$E\%G@B\&D$
This can be broken down into individual relations:
• 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 (implies "Some B are D" and "Some B are not D").

Step 2: Evaluating the Conclusions

• Conclusion I: All B being D is a possibility
From the statement $B\&D$ (Only a few B are D), we know for certain that some part of B is not D. Because of this restriction, all B can never be D. Thus, this possibility is invalid.
(Conclusion I does not follow)

• Conclusion II: Some B being C is not a possibility
There is no direct negative relationship defined between B and C. The only constraint is that the part of B that overlaps with E (since All G are B and Some G is E) cannot be C. However, the remaining part of B can still overlap with C. Therefore, "Some B being C" is a valid possibility. Saying that it is "not a possibility" is incorrect.
(Conclusion II does not follow)

• Conclusion III: All G can never be C
We know that "Some G is E" ($E\%G$) and "No C is E" ($C\$E$). This means the portion of G that is common with E can never be C. Since at least some part of G can never be C, it is impossible for all G to be C.
(Conclusion III follows)

• Conclusion IV: All D can be E
There is no negative relationship or constraint preventing the entire set D from being inside E. Hence, all D being E is a possibility.
(Conclusion IV follows)

Therefore, only conclusions III and IV logically follow.