Given the following statements : S1 : If L is a regular language then the…

Answer: S1 is correct and S2 is not correct.

S1 — Reason: If L is regular then the reversal L^R is regular (regular languages are closed under reversal). The concatenation of two regular languages is regular, so {uv | u ∈ L, v ∈ L^R} equals L · L^R and is regular.

S2 — Reason: The language {ww^R | w ∈ Σ*} is the set of even-length palindromes (each string is a string followed by its reverse). For alphabets with at least two symbols this language is not regular because it requires matching an arbitrary-length first half with the second half; this can be formalized using the pumping lemma or Myhill–Nerode theorem. (Note: over a unary alphabet the language becomes the set of all even-length strings, which is regular; but the general statement without restricting the alphabet is false.)