1. Design a PDA with proper comments to accept each of the following languages by empty stack model. NO credit will be given if you design a CFG and then convert it to the equivalent PDA. (a) {abck | m+k=n, where n, m, k>0} (b) {a"bek | n+k=m, where n, m, k>0} (c) (01|3i4j, where i and j > 0} (d) {we (a,b,c) | #a(w) + #b(w) = #c(w)} (e) Let= {a,b,c) and let L be the language of all words in which all the a's come before the b's and there are the same number of a's as b's and arbitrarily many c's that can be in front, behind, or among the a's and b's. Some words in L are , abc, caabcb, ccacaabcccbccbc.