Write a JAVA program that solves the following problem.

Please include:

a. Instructions, if any, required to use the program, enter values, etc.

b. Cases in which the program will fail with examples, if any.

c. A flowchart and description of how the program works.

1. Given a compound propositional logic statement, give the following as an output:

a. A truth table for the expression starting from individual propositional logic statements and showing all intermediate steps.

b. A simplified version of the statement (ONLY if it is possible to simplify the expression using inference rules)

Below is an example of an input and output.

Example: Input: [PA (q r)]-> (q r) Output: a. Truth table with all intermediate steps b. Simplified Expression: T (the given expression is a Tautology) Example: Input: [PA (q r)]-> (q r) Output: a. Truth table with all intermediate steps b. Simplified Expression: T (the given expression is a Tautology)