Given the following symbol meanings between two numbers *x* and *y*: - *x % y* means *y* is neither smaller nor greater than *x* (i.e., *y = x*) - *x & y* means *y* is neither greater nor equal to *x* (i.e., *y x*) - *x $ y* means *y* is not greater than *x* (i.e., *y ≤ x*) - *x α y* means *y* is not smaller than *x* (i.e., *y ≥ x*) Analyze the following statements: - U $ L α K % T - W & P - D * J - W % R $ L - M * T α J Which of the following conclusions is/are true? I. M * W II. D & K III. J $ P

Question

Given the following symbol meanings between two numbers *x* and *y*:

- *x % y* means *y* is neither smaller nor greater than *x* (i.e., *y = x*)
- *x & y* means *y* is neither greater nor equal to *x* (i.e., *y < x*)
- *x * y* means *y* is neither smaller nor equal to *x* (i.e., *y > x*)
- *x $ y* means *y* is not greater than *x* (i.e., *y ≤ x*)
- *x α y* means *y* is not smaller than *x* (i.e., *y ≥ x*)

Analyze the following statements:

- U $ L α K % T
- W & P
- D * J
- W % R $ L
- M * T α J

Which of the following conclusions is/are true?

I. M * W

II. D & K

III. J $ P

Accepted Answer

**Solution:** 1. First, interpret the given symbols: - *x % y* means *y = x* - *x & y* means *y < x* - *x * y* means *y > x* - *x $ y* means *y ≤ x* - *x α y* means *y ≥ x* 2. Analyze each conclusion: - I. M * W means W > M - From the statements, M * T α J means T > M and J ≥ T - But no direct relation between M and W is given; hence M * W cannot be confirmed true. - II. D & K means K < D - From D * J, J > D - No direct relation between D and K is given; so D & K cannot be confirmed true. - III. J $ P means P ≤ J - From W & P, P < W - From W % R $ L, R = W and L ≤ R - No direct relation between J and P is given; so J $ P cannot be confirmed true. 3. Since none of the conclusions can be established as true based on the given statements, the correct answer is: **Answer:** None is true

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