Formally proof that the class of regular languages is closed under reverse: For any string w = w1w2...wn, the reverse of w is denoted by w^(R) = wnwn-1...w1. For any regular language L, proof that L^(R) = { w^(R)| w L } is also regular.

6.

5. (5 Points) Closure Properties Formally proof that the class of regular languages is closed under reverse: For any string w = W1W2...W7z, the reverse of w is denoted by w* = WWr-1...W. For any regular language L, proof that LR = { WRW EL } is also regular. 6. (5 points BONUS) Closure Properties: Bonus Formally proof that the class of regular languages is closed under perfect shuffle: Given two lan- guages, LA and Le over alphabet , the perfect shuffle is defined as {w w = 2161...Qzby, where QyE LA and bi E Le and only by E ). For this to work, you can assume that each string of LA and LB has the same length, namely k