A program has the following rule:

a :$-$ b$1,$ b$2,$ not c$.$

c :$-$ not a$.$

Atoms $"$a$"$ and $"$c$"$ do not occur in any other rule.

What of the following are true?

If b$1$ is false in a stable model, then a is also false in that stable model.

If b$2$ is false in a stable model, then a is also false in that stable model.

If $b1$ and $b2$ are false in a stable model, then $a$ is also false in that stable model.

If b$1$ and b$2$ are true in a stable model, then a is also true in that stable model.

If b$1$ and b$2$ are true in a stable model, then there no stable model where a true.