Pick out the true statements:
a. Let $R$ be a commutative ring with identity. Let $M$ be an ideal such that every element of $R$ not in $M$ is a unit. Then $R/M$ is a field.
b. Let $R$ be as above and let M be an ideal such that $R/M$ is an integral domain. Then $M$ is a prime ideal.
c. Let $R = C[0, 1]$ be the ring of real-valued continuous functions on $[0, 1]$ with respect to pointwise addition and pointwise multiplication. Let $M = \{ f ∈ R \mid f(0) = f(1) = 0 \}$. Then $M$ is a maximal ideal.
Certainly (b) is true but no idea about (a) and (c).