Tessellate S.T.E.M.S. (2019) - Computer Science - College - Set 3 - Objective Problem 4

Let $\Sigma$ be a finite alphabet and let $L_1, L_2, L_3 \subseteq \Sigma^{*}$ be three languages. Which of the following statements is always true?

• A) $L_1.(L_2 \cap L_3) = L_1.L_2 \cap L_1.L_3$
• B) $L_1^{*} = \{\epsilon\}$ if and only if $L_1 = \{\epsilon\}$
• C) $L_1.(L_2 \cup L_3) = L_1.L_2 \cup L_1.L_3$
• D) $(L_1.L_2)^{R} = (L_1)^{R}.(L_2)^{R}$

This problem is a part of Tessellate S.T.E.M.S (2019)