A is correct (definition of equivalence relation). B is incorrect: f(x)=ex is one-one since f′(x)=ex>0. C is correct (injective = one-one). D is treated as correct (intended meaning: surjective = onto). E is incorrect: many-one means two elements have the same image, not different images. So A, C, D only.
Note: Option D uses 'subjective' which is taken as the intended term 'surjective'.