Probability Distribution

[Dreyfus]

Acc to me if X is continuous rv then a and b must be true but c will be false
And if I assume that X is discrete there can be monotonically increasing step function then a will definitely false and b will also false as in interval [b,c) F(x) is horizontal so there can be case that b is largest value x can take so it should be option c ...
Am I right or wrong? Please comment..