1. Given: One mole of an ideal gas. We check each statement.

2. Statement (a): $U$ and $H$ each depend only on temperature.

For an ideal gas, $U = U(T)$ and since $H = U + PV = U + RT$ for one mole of ideal gas, $H$ also depends only on $T$.

So, (a) is true.

3. Statement (b): Compressibility factor $z$ is not equal to $1$.

Compressibility factor is $z = \frac{PV}{nRT}$ For an ideal gas, $PV = nRT \implies z = 1$ So the statement "$z$ is not equal to $1$" is false.

Thus, (b) is false.

4. Statement (c): $C_{P,m} - C_{V,m} = R$

For an ideal gas, Mayer’s relation holds: $C_{P,m} - C_{V,m} = R$ Hence, (c) is true.

5. Statement (d): $dU = C_V dT$ for any process.

For an ideal gas, internal energy depends only on temperature. Therefore, $dU = \left(\frac{\partial U}{\partial T}\right)_V dT = C_V dT$ Since $U$ is a function only of $T$, this differential holds for any process.

Thus, (d) is true.

6. Collecting results:

• (a) True
• (b) False
• (c) True
• (d) True

So the correct set is: $\boxed{(a), (c) \text{ and } (d)}$

Therefore, the correct option is: $\boxed{A}$

7. Comparison with stored answer: Stored correct answer = A.

My derived answer = A. So, they agree.