For each of the following problems, decide whether the set A is regular. If the set is regular, give a FSM that recognizes it; if the set is not regular, prove it using the pumping lemma, l. A { sl ls l s E {0} *} Thus the strings 0001 1000 and 000001 100000 are elements of A, but 00100 and 001100000 are not. 2. A={rils I r's E {0}*) Thus the strings 001100 and 0110000 are elements of A, but 00111100 and 000010 are not. 3A= {w E {a,b} * I w contains at least two a's and at most two b's 4. A- (w E (a,b*w contains exactly two more a's than b's; 5. A= { 30n1n2n4 In>1) Thus 30011224 and 30001112224 are elements of A but 301124, 3001122, 0001112224, and 301224 are not. 6. A= {3OPIq24 I p>-l, q>=1, r>-1 } Thus 30124 and 3001 22224 are elements of A but 30120124, 301122, and 3010124 are not. 7. A= {w E {0,1}* l there are 3 times as many O's as l's. 8. A-{w E 0,1,2,3}* I at least half the symbols comprising w are O's) 9. A= { sE { a,b,c} * l s is a palindrome. (A palindrome is a string of characters that reads the same forward as backwards - ie., s - reverse(s) for the string s. Examples of palindromes are the words mom, deed, and otto. 10. A- {rs E (0,1,2* I r is a proper prefix of s} Thus 010010112 and 20122012110 are elements of A, but 01002 and 211020111 are not