Step 1: Understand nucleic acid bases.
DNA contains bases adenine, guanine, cytosine, and thymine. RNA contains adenine, guanine, cytosine, and uracil instead of thymine.
Step 2: Evaluate statement (a).
DNA does not contain uracil; it contains thymine instead. Hence (a) is correct.
Step 3: Evaluate statement (b).
RNA does not contain thymine; it uses uracil in place of thymine. Hence (b) is correct.
Step 4: Evaluate statement (c).
Both DNA and RNA do NOT contain uracil simultaneously; DNA lacks uracil. Hence (c) is incorrect.
Step 5: Evaluate statement (d).
RNA does not contain both uracil and thymine; it contains only uracil. Hence (d) is incorrect.
Step 6: Final conclusion.
Only statements (a) and (b) are correct.
Final Answer:
\[
\boxed{a,\ b}
\]