In a symbolic direction notation, "A x B" means A is to the South of B, "A + B" means A is to the North of B, "A % B" means A is to the East of B and "A - B" means A is to the West of B. In the expression P % Q + R - S, in which direction is S located with respect to Q?

Introduction:
This question uses symbolic notation to describe relative directions between points or persons. Different symbols represent "south of", "north of", "east of" and "west of". We must interpret a combined expression P % Q + R - S and then determine the direction of S with respect to Q. The key is to decode each relation carefully and then place all points on a coordinate grid.

Given Data / Assumptions:
• A x B: A is to the South of B.• A + B: A is to the North of B.• A % B: A is to the East of B.• A - B: A is to the West of B.• Expression: P % Q + R - S.• We are asked: In which direction is S with respect to Q?

Concept / Approach:
We interpret each relation pairwise. For example, P % Q means P is to the East of Q. Working left to right, we express all points in terms of Q. Once we know the relative positions of P, R and S on an x–y coordinate grid, we can compute the displacement from Q to S and identify the corresponding direction (such as North-East, South-West, etc.).

Step-by-Step Solution:
Step 1: Decode P % Q. The symbol % means "to the East of", so P is to the East of Q.Step 2: Decode Q + R. The symbol + means "to the North of", so Q is to the North of R. Equivalently, R is to the South of Q.Step 3: Decode R - S. The symbol - means "to the West of", so R is to the West of S. Equivalently, S is to the East of R.Step 4: Introduce coordinates. Place Q at (0, 0) for convenience.Step 5: Since Q is North of R, R must be South of Q, so we can place R at (0, −1).Step 6: Since S is to the East of R, we place S at (1, −1).Step 7: Now view S relative to Q. From Q at (0, 0) to S at (1, −1) the displacement is (1, −1), that is, 1 unit East and 1 unit South.Step 8: A movement combining East and South corresponds to the South-East direction.

Verification / Alternative check:
We can also reason qualitatively without coordinates. Since R is South of Q, draw R below Q. Because S is East of R, draw S to the right of R. This places S diagonally below and to the right of Q, which is exactly South-East of Q. Thus, either with coordinates or a diagram, the outcome is the same.

Why Other Options Are Wrong:
South-West would place S below and to the left of Q, which is inconsistent because S was placed to the right (East) of R and R is already South of Q. North-East would be above and to the right of Q, but S lies below Q. North-West would be above and to the left, again contradicting the description. The option "East" alone would ignore the fact that S is also South of Q.

Common Pitfalls:
Students sometimes read P % Q + R - S as if it were an arithmetic expression and try to combine symbols algebraically. Instead, each pair must be interpreted as a separate directional relation. Another mistake is to reverse the direction, for example reading "A % B" as "B is East of A". Carefully noting which element is on the left of a symbol and which is on the right helps avoid this error.

Final Answer:
In the expression P % Q + R - S, point S is located to the South-East of Q.