Find the detailed proof below.

Part (a) Video Solution

Part (b) Video Solution

(a):

$(L_1 \cup L_2)^R = \{ x^R | \,\, x \in L_1 \cup L_2 \}$

$(L_1 \cup L_2)^R = \{ x^R | \,\, x \in L_1 \} \cup $ $\{ x^R | \,\, x \in L_2 \}$

$(L_1 \cup L_2)^R = L_1^R \cup L_2^R$

(b):