Let 𝑆 be the set of all complex numbers z satisfying $$|z^{2} + z + 1| = 1$$. Then which of the following statements is/are TRUE?

A

$$\left|z + \frac{1}{2}\right| \leq \frac{1}{2}$$ for all $$z \epsilon S$$

B

$$\left|z\right| \leq 2$$ for all $$z \epsilon S$$

C

$$\left|z + \frac{1}{2}\right| \geq \frac{1}{2}$$ for all $$z \epsilon S$$

D

The set S has exactly four elements