Directional Reasoning Analysis

This problem requires understanding coded directional relationships and applying them sequentially to find the final direction of one point relative to another.

Decoding Directional Codes

First, let's interpret the given codes based on the provided definitions:

• $P % Q$ means Q is to the North-East of P.
• $P & Q$ means Q is to the South of P.
• $P ^ Q$ means Q is to the East of P.

Applying Codes to the Expression

Now, apply these codes to the expression $D % B & C ^ A$ step-by-step:

1. D % B: This means B is North-East of D.
2. B & C: This means C is South of B.
3. C ^ A: This means A is East of C.

Visualizing the Relative Positions

Let's determine the position of A relative to D:

• Start at point D.
• From D, move North-East to reach B.
• From B, move South to reach C. Since C is South of B, and B is North-East of D, C will end up being directly East of D.
• From C, move East to reach A. Since A is East of C, and C is East of D, A will be further East of D.

Example using coordinates:

• Let D be at (0,0).
• B (North-East of D) is at (1,1).
• C (South of B) is at (1,0). Note: (1,0) is East of (0,0).
• A (East of C) is at (2,0).

Final Direction Determination

Comparing the position of A (2,0) with D (0,0), A is located horizontally to the right of D.

Therefore, A is in the East direction with respect to D.