Question $1$: Equivalence and Satisfiability For each statement s$1$s$4,$ you are to: $1\mathrm{.}1$ : Write the truth table for the statement $($optional and unmarked $)1\mathrm{.}2$ : Determine equivalence of statements by comparing their respective truth tables $(1$pt$)1\mathrm{.}3$ : State a model that is satisfied by one group of statements and that is not satisfied by any of the other statements $(1$pt$)$ For this question, you need to create a folder that contains four files; you will put your computer$-$readable answers in your Python script named a$2.$py$.$ The folder will contain all of your answers to Question $1\mathrm{.}1.$ The script will contain your answers to Question $1\mathrm{.}2,$ Question $1\mathrm{.}3,$ and Question $2.$ The answers to Question $1\mathrm{.}1$ will be files that are named a$2$q$1$a$$a$2$q$1$d$.$ These can be text files, pictures of hand$-$written answers, or any other format. They are optional but will be extremely helpful to solving $1\mathrm{.}2$ and $1\mathrm{.}3.$ The answers to Question $1\mathrm{.}2$ and Question $1\mathrm{.}3$ will be in your Python script. The script will include the definition of two variables, a$2$q$12$ and a$2$q$13.$ For Question $1\mathrm{.}2,$ statement equivalence, the variable a$2$q$12$ will be a list of lists that group together the equivalent statements. These examples are incorrect but illustrate how to answer: #a$2$q$12=[[$s$1,$s$2,$s$3,$s$4]]$ # they are all equivalent. #a$2$q$12=[[$s$1],[$s$2],[$s$3],[$s$4]]$ # they are all different #a$2$q$12=???$ # the right answer please! For Question $1\mathrm{.}3,$ statement satisfiability, your answer will be a dictionary mapping variables to True or False. Use all and only the variables in your individualized problem set. An example answer, which is almost certainly incorrect, is a$2$q$13=\{$ P: True, Q: False, R: True, S: False, T: True $\}$