Decoding the Directional Coding Language

The problem provides a unique coding language to describe the relative positions of points. We need to first understand this language to determine the actual distances and directions.

Let's decode the rules:

• P 17@ Q means P is 14 m north to Q. Here, 14 = 17 - 3.
• P 15$ Q means P is 20 m east to Q. Here, 20 = 15 + 5.
• P 16% Q means P is 13 m south to Q. Here, 13 = 16 - 3.
• P 12& Q means P is 17 m west to Q. Here, 17 = 12 + 5.

Based on these examples, the rule for calculating distance seems to be:

• For '@' (North) and '%' (South): Distance = Given Number - 3
• For '$' (East) and '&' (West): Distance = Given Number + 5

Now, let's apply these rules to the given positions of the points:

• A 15& B: A is 15 + 5 = 20 m West of B. (B is 20m East of A)
• B 27% C: B is 27 - 3 = 24 m South of C. (C is 24m North of B)
• C 17& D: C is 17 + 5 = 22 m West of D. (D is 22m East of C)
• L 18% A: L is 18 - 3 = 15 m South of A. (A is 15m North of L)
• M 33$ L: M is 33 + 5 = 38 m East of L. (L is 38m West of M)
• N 28@ M: N is 28 - 3 = 25 m North of M. (M is 25m South of N)
• O 15$ N: O is 15 + 5 = 20 m East of N. (N is 20m West of O)
• K 17@ O: K is 17 - 3 = 14 m North of O. (O is 14m South of K)

Mapping Point Positions using Coordinates

To verify the expressions, let's establish a coordinate system. We can place point A at the origin (0,0) for ease of calculation.

• A: (0, 0)
• L is 15m South of A: L is at (0, 0 - 15) = (0, -15)
• M is 38m East of L: M is at (0 + 38, -15) = (38, -15)
• N is 25m North of M: N is at (38, -15 + 25) = (38, 10)
• O is 20m East of N: O is at (38 + 20, 10) = (58, 10)
• K is 14m North of O: K is at (58, 10 + 14) = (58, 24)
• A is 20m West of B means B is 20m East of A: B is at (0 + 20, 0) = (20, 0)
• B is 24m South of C means C is 24m North of B: C is at (20, 0 + 24) = (20, 24)
• C is 22m West of D means D is 22m East of C: D is at (20 + 22, 24) = (42, 24)

Here is a summary of the point coordinates:

Verifying the Given Expressions

We will now evaluate each expression provided in the options to see if it is true or false based on our calculated coordinates and the coding rules.

Option 1: C 33& K

According to the coding rules, C 33& K means C is 33 + 5 = 38 m West of K.

Let's check the coordinates:

• C is at (20, 24)
• K is at (58, 24)

The difference in x-coordinates is 58 - 20 = 38. The difference in y-coordinates is 24 - 24 = 0. Since the y-coordinates are the same and the x-coordinate of K (58) is greater than the x-coordinate of C (20), K is 38m East of C. This means C is 38m West of K.

This statement is True.

Option 2: N 15& O

According to the coding rules, N 15& O means N is 15 + 5 = 20 m West of O.

Let's check the coordinates:

• N is at (38, 10)
• O is at (58, 10)

The difference in x-coordinates is 58 - 38 = 20. The difference in y-coordinates is 10 - 10 = 0. Since the y-coordinates are the same and the x-coordinate of O (58) is greater than the x-coordinate of N (38), O is 20m East of N. This means N is 20m West of O.

This statement is True.

Option 3: O 17% K

According to the coding rules, O 17% K means O is 17 - 3 = 14 m South of K.

Let's check the coordinates:

• O is at (58, 10)
• K is at (58, 24)

The difference in x-coordinates is 58 - 58 = 0. The difference in y-coordinates is 24 - 10 = 14. Since the x-coordinates are the same and the y-coordinate of K (24) is greater than the y-coordinate of O (10), K is 14m North of O. This means O is 14m South of K.

This statement is True.

Option 4: A 18@ L

According to the coding rules, A 18@ L means A is 18 - 3 = 15 m North of L.

Let's check the coordinates:

• A is at (0, 0)
• L is at (0, -15)

The difference in x-coordinates is 0 - 0 = 0. The difference in y-coordinates is 0 - (-15) = 15. Since the x-coordinates are the same and the y-coordinate of A (0) is greater than the y-coordinate of L (-15), A is 15m North of L.

This statement is True.

We have evaluated options 1, 2, 3, and 4, and found all of them to be true statements based on the provided coding rules and point positions. The question asks which of the following expressions is false.

Since none of the expressions (1, 2, 3, 4) are false, the correct answer is that none of these expressions are false.

Therefore, the expression that is false is represented by the option stating "None of these" if all individual expressions are true. Our analysis shows all options 1-4 are true.