Design and implement an application that simulates the customers waiting in line at a bank. use a queue data structure to represent the line. as customers arrive at the bank, customer objects are put in the rear of the queue with an enqueue opera-tion. when the teller is ready to service another customer, the customer object is removed from the front of the queue with a dequeue operation. randomly determine when new custom-ers arrive at the bank and when current customers are finished at the teller window. print a message each time an operation occurs during the simulation.

Sometimes writers elaborate on the truth when recalling past events so they can enhance their narrative essay with more interesting descriptions. do you feel that published writers should or should not embellish real life events just to make their stories more interesting?

Convert and simplify the following sentences to conjunctive normal form (cnf): (a) (p → (q → r)) → (p → (r → q)) (b) (p ∧ q) → (¬p ↔ q) (c) ((p → q) ∧ ¬q) → ¬p

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.