The expression given is $\phi(\phi(30))$, where $\phi$ denotes the Euler's Totient function. The Totient function $\phi(n)$ is defined as the number of positive integers up to $n$ that are coprime to $n$.

1. Calculate $\phi(30)$:

   • $30 = 2 \times 3 \times 5$, so using the formula for the Totient function: $\phi(30) = 30 \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{5}\right)$ $= 30 \times \frac{1}{2} \times \frac{2}{3} \times \frac{4}{5} = 30 \times \frac{8}{30} = 8$ So, $\phi(30) = 8$.

2. Calculate $\phi(8)$:

   • $8 = 2^3$, so: $\phi(8) = 8 \left(1 - \frac{1}{2}\right) = 8 \times \frac{1}{2} = 4$ Therefore, $\phi(\phi(30)) = \phi(8) = 4$.

The correct answer is (a) 4.

Would you like more details or have any questions?

Here are some related questions:

1. How does Euler's Totient function work for composite numbers with multiple prime factors?
2. What is the Totient function value for other small numbers like 12 or 15?
3. How does the Totient function apply in cryptography?
4. Can Euler's Totient function be used in modular arithmetic?
5. How is the Totient function related to prime numbers?

Tip: Understanding the Totient function helps in number theory, especially in fields like cryptography.