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Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

4. what is the reason for including the following code snippet in the header file animal.h? #ifndef animal_h #define animal_h class animal { public: animal(); animal(double new_area_hunt); void birth(); void hunt(double new_area_hunt); void death(); double get_area_hunt() const; private: double area_hunt; }; #endif

Consider the usual algorithm to convert an infix expression to a postfix expression. suppose that you have read 10 input characters during a conversion and that the stack now contains these symbols: (5 points) | | | + | | ( | bottom |_*_| now, suppose that you read and process the 11th symbol of the input. draw the stack for the case where the 11th symbol is