Study the following information carefully to answer the related question:

- $X\#Y$ means $X$ is $11 ext{ m}$ north to $Y$
- $X\€Y$ means $X$ is $7 ext{ m}$ east to $Y$
- $X\alpha Y$ means $X$ is $6 ext{ m}$ west to $Y$
- $X@Y$ means $X$ is $13 ext{ m}$ south to $Y$
- $X\%Y$ means $X$ is $9 ext{ m}$ west to $Y$
- $X\Omega Y$ means $X$ is $8 ext{ m}$ south to $Y$

If '$M\#A\alpha B@S\%R\€N$' holds true, then which among the following points do **not** lie in the southwest of $N$?

Question

Study the following information carefully to answer the related question:

- $X\#Y$ means $X$ is $11 	ext{ m}$ north to $Y$
- $X\€Y$ means $X$ is $7 	ext{ m}$ east to $Y$
- $X\alpha Y$ means $X$ is $6 	ext{ m}$ west to $Y$
- $X@Y$ means $X$ is $13 	ext{ m}$ south to $Y$
- $X\%Y$ means $X$ is $9 	ext{ m}$ west to $Y$
- $X\Omega Y$ means $X$ is $8 	ext{ m}$ south to $Y$

If '$M\#A\alpha B@S\%R\€N$' holds true, then which among the following points do **not** lie in the southwest of $N$?

Accepted Answer

**Solution:**

We are given the expression:

$$M \# A \alpha B @ S \% R \€ N$$

where the symbols represent relative directions and distances:

- $X \# Y$: $X$ is 11 m north of $Y$
- $X \€ Y$: $X$ is 7 m east of $Y$
- $X \alpha Y$: $X$ is 6 m west of $Y$
- $X @ Y$: $X$ is 13 m south of $Y$
- $X \% Y$: $X$ is 9 m west of $Y$
- $X \Omega Y$: $X$ is 8 m south of $Y$

We need to find which points do **not** lie southwest of $N$.

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**Step 1: Understand the chain and find relative positions**

The chain is:

$$M \# A \alpha B @ S \% R \€ N$$

This means:

- $M \# A$: $M$ is 11 m north of $A$  
- $A \alpha B$: $A$ is 6 m west of $B$  
- $B @ S$: $B$ is 13 m south of $S$  
- $S \% R$: $S$ is 9 m west of $R$  
- $R \€ N$: $R$ is 7 m east of $N$

We want to find the coordinates of each point relative to $N$.

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**Step 2: Assign coordinate system**

Let’s place $N$ at origin $(0,0)$.

- Since $R \€ N$ means $R$ is 7 m east of $N$, so:
  $$R = (0 + 7, 0) = (7, 0)$$

- $S \% R$ means $S$ is 9 m west of $R$:
  $$S = (7 - 9, 0) = (-2, 0)$$

- $B @ S$ means $B$ is 13 m south of $S$:
  $$B = (-2, 0 - 13) = (-2, -13)$$

- $A \alpha B$ means $A$ is 6 m west of $B$:
  $$A = (-2 - 6, -13) = (-8, -13)$$

- $M \# A$ means $M$ is 11 m north of $A$:
  $$M = (-8, -13 + 11) = (-8, -2)$$

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**Step 3: Check which points lie southwest of $N$**

- Southwest means both x-coordinate and y-coordinate are negative relative to $N$.

- Coordinates relative to $N$:
  - $M = (-8, -2)$  (x < 0, y < 0) → Southwest
  - $A = (-8, -13)$ (x < 0, y < 0) → Southwest
  - $B = (-2, -13)$ (x < 0, y < 0) → Southwest
  - $S = (-2, 0)$   (x < 0, y = 0)  → Not strictly southwest (y is not negative)

Therefore, $S$ does **not** lie southwest of $N$.

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**Step 4: Verify options**

Options:
- (a) M → lies southwest
- (b) B → lies southwest
- (c) S → does not lie southwest
- (d) A → lies southwest
- (e) Either ‘S’ or ‘M’ → only $S$ does not lie southwest, $M$ does

**Answer:** Option (c) $S$

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**Final conclusion:**

The point which does **not** lie southwest of $N$ is **S**.

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