Final answer:
Activation of the SOS response in a bacterium infected with a prophage mainly leads to mutation of the bacterial DNA, rather than immediate destruction of viral genes or complete lysis of the bacterial culture.
Step-by-step explanation:
The activation of the SOS system in a bacterium infected with a prophage results in mutation of the DNA (Option C). The SOS response is a complex regulatory network that is activated in response to DNA damage, which can result in the induction of error-prone DNA polymerases leading to mutations. This activation does not target the viral genes for destruction nor does it necessarily result in complete lysis of the bacterial culture. It primarily affects the bacterial DNA and can sometimes cause the prophage to excise from the bacterial genome and enter into the lytic cycle, which could ultimately lead to lysis of the bacterium. However, the key effect of the SOS response is the potential for mutations to occur, rather than an immediate lysis or destruction of viral repressor proteins.