Use logical equivalences to perform a direct proof that the two following logical statements are equivalent. Statement 1: !(P OR (!P AND Q)) Statement 2: !P AND !Q

1) Simplify the following Boolean expressions to a minimum number of literals correctly: (a + b + c')(a' b' + c) 2) Simplify the following Boolean expressions to a minimum number of literals: a'bc + abc' + abc + a'bc' 3) Simplify the following Boolean expressions to a minimum number of literals: xy + x(wz + wz')

-Using the previous example given in the photos. Please give a similar example (not the same one as photos) of a simple program using 2 variables that require user input, two constants that are initialized upon declaration, and either a decision or repetition control structure the program uses to control the flow of logic. 1) Provide a hand-tracing example that tests the program like previous example and explain the process. Thank you! Will give rating.

2. Boolean Algebra