in Theory of Computation
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Prove or disprove the following claims.
(a) $(L_1 ∪ L_2)^R = L_1^R ∪ L_2^R$ for all languages $L_1$ and $L_2$.
(b) $(L^R)^* = (L^*)^R$ for all languages $L$.
in Theory of Computation
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(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 $ $\{ x^R | \,\, x \in L_2 \}$

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

Part (a) Video Solution

(b):

Part (b) Video Solution

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