- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
Answer: D
Explanation
Let’s translate the given symbols:
P: >
Q: 8z.
From 3x = 4z, we can express x in terms of z: x = 4z/3.
Substitute this into the first inequality: 2(4z/3) ≥ 3y
8z/3 ≥ 3y
Multiply by 3: 8z ≥ 9y.
The conclusion given is 9y > 8z. This contradicts our derived inequality (8z ≥ 9y), as 9y cannot be strictly greater than 8z if 8z is greater than or equal to 9y. Thus, Statement 1 is incorrect.
**Statement 2: If x(Q)2y and y(R)z, then x(R)z.**
Translate: If x < 2y and y ≤ z, then x ≤ z.
From y ≤ z, we can infer that 2y ≤ 2z.
We have two inequalities: x < 2y and 2y ≤ 2z.
Combining these, we get x < 2z.
The conclusion given is x ≤ z. However, x < 2z does not necessarily imply x ≤ z. For example, if x=3 and z=2, then x < 2z (3 < 4) is true, but x ≤ z (3 ≤ 2) is false. Thus, Statement 2 is incorrect.
Therefore, neither Statement 1 nor Statement 2 is correct. This question tests logical reasoning with inequalities and symbolic representation.