Can a monoalphabetic substitution cipher attain perfect secrecy? Can a monoalphabetic substitution cipher attain perfect secrecy?

Definition of perfect secrecy:

$${\rm Pr}[\,{\rm Enc}_k(m_1) = c\,] = {\rm Pr}[\,{\rm Enc}_k(m_2) = c\,]$$
Since this is homework, let me just give you a hint: consider the two-character messages $m_1 = \text{"aa"}$ and $m_2 = \text{"ab"}$.

Given a ciphertext $c$ encrypted with a monoalphabetic substitution cipher, can you tell which of $m_1$ or $m_2$ it corresponds to, even without knowing the key?  Why (not)?  What does this imply about perfect secrecy?



Ps. The hint I gave above assumes that the cipher is not homophonic, i.e. that the encryption of each character is deterministic and independent of its position or the presence of other characters in the message.  For a (possibly) homophonic monoalphabetic cipher, it may be simpler to start the argument from the other end: if you intercept the ciphertext $c = \text{"xx"}$, what can you say about the plaintext?