In the following questions, the symbols %, @, &, $ and # are used with the following meanings:

- $: 'A$B' means 'A is not greater than B'
- %: 'A%B' means 'A is not smaller than B'
- @: 'A@B' means 'A is neither smaller nor greater than B'
- &: 'A&B' means 'A is neither equal to nor smaller than B'
- #: 'A#B' means 'A is neither equal to nor greater than B'

Given the statements:

- P&Q#U$W
- Q%S&T
- W#Y@Z

Evaluate the following conclusions:

I. Q#Z
II. S&W
III. P%Y

Assuming the statements are true, which of the conclusions is/are definitely true?

Question

In the following questions, the symbols %, @, &, $ and # are used with the following meanings:

- $: 'A$B' means 'A is not greater than B'
- %: 'A%B' means 'A is not smaller than B'
- @: 'A@B' means 'A is neither smaller nor greater than B'
- &: 'A&B' means 'A is neither equal to nor smaller than B'
- #: 'A#B' means 'A is neither equal to nor greater than B'

Given the statements:

- P&Q#U$W
- Q%S&T
- W#Y@Z

Evaluate the following conclusions:

I. Q#Z
II. S&W
III. P%Y

Assuming the statements are true, which of the conclusions is/are definitely true?

Accepted Answer

**Solution:** Let's analyze the given statements and conclusions step-by-step using the symbol meanings: 1. **Given Statements:** - P&Q#U$W - Q%S&T - W#Y@Z 2. **Break down each statement:** - *P&Q#U$W* means: - P&Q: P is neither equal to nor smaller than Q → P > Q - Q#U: Q is neither equal to nor greater than U → Q < U - U$W: U is not greater than W → U ≤ W - *Q%S&T* means: - Q%S: Q is not smaller than S → Q ≥ S - S&T: S is neither equal to nor smaller than T → S > T - *W#Y@Z* means: - W#Y: W is neither equal to nor greater than Y → W < Y - Y@Z: Y is neither smaller nor greater than Z → Y = Z 3. **Analyze conclusions:** - I. Q#Z: Q is neither equal to nor greater than Z → Q < Z - From above, Q < U ≤ W < Y = Z - So, Q < Z is true. - II. S&W: S is neither equal to nor smaller than W → S > W - From above, S > T, but no direct relation between S and W is given. - Since W < Y = Z and S > T, no conclusive relation between S and W. - So, II is not definitely true. - III. P%Y: P is not smaller than Y → P ≥ Y - From above, P > Q < U ≤ W < Y - Since P > Q and Q < U ≤ W < Y, P is less than Y or unknown, so P ≥ Y is not certain. 4. **Conclusion:** Only conclusion I is definitely true. **Answer:** Only I is true

Answer

Answer

Answer

Answer