3. (40 points) Give a predicate that exactly characterizes each of the following sets of strings. That is to say, your predicate should have a free variable (say w), and should hold if and only if w is instantiated to a string in the set. (a) Strings containing both 101 and 010. (b) Strings that contain 101 if they contain 10. (c) Strings that contain the substring 11 in two different ways. (So 111 is included, but 011 is not.) (d) Strings that contain at least four 1s. 3. (40 points) Give a predicate that exactly characterizes each of the following sets of strings. That is to say, your predicate should have a free variable (say w), and should hold if and only if w is instantiated to a string in the set. (a) Strings containing both 101 and 010. (b) Strings that contain 101 if they contain 10. (c) Strings that contain the substring 11 in two different ways. (So 111 is included, but 011 is not.) (d) Strings that contain at least four 1s