Give the regular expression that generate each of the following languages. In all cases, the alphabet is ={a,b} i. The language {w{a+b} last two symbols in w are not same }. ii. The language {ww contains at least two a 's, or exactly two b 's }. iii. The language {w every a in w is followed by at least one b}. iv. Strings of a's and b's with at-most one pair of consecutive a's. v. Strings of a's and b's with no consecutive b's. vi. L={vwvv,w and vmod3=0}. Draw the DFAs for the following languages over the alphabet ={a,b}. [4] i. A DFA for the language L={w{a+b}na(w)2,nb(w)1}.[Hint: na(w) means number of a 's in the string w ]. ii. A DFA for G={w{a+b}w2 and second-to-last symbol of w is b}. Prove the following [2] i. +1(011)(1(011))=(1+011) ii. (1+001)+(1+001)(0+101)(0+101)=01(0+101)