Program 3 We have the following tautology from De Morgan's Laws: ~(PAQ) = (~P) V(~Q) Prove the tautology by using your program to construct the lexicographical possible truth values for p and q. Then create intermediate columns for binary operations such as ( P Q) and then ~(PAQ) " using the and, or, and not operators in python and your functions for implies and if and only if your created in program 2. End with the binomial operation of (left side of equation) if and only if (right side of equation). An example of what your output might look like is shown below. I--0-- --1--|--2--1--3--|--4--1--5--1--6--|--7--1 |--------I-PQ-IN(PQ) I-NP-|--NQ-NPVNQI-iff- - - - - - - - - - - - - - - - - - - True True True False False False False True ----- ----- ----- ----- ----- ----- ----- ----- True False False True False True True True - - - - - - - - - - - - - - - - - - - - - - - - - - - False True False True True False True True ! +------------------------- ----- -----+ ---+ False False False True True True True True >>> Program 3 We have the following tautology from De Morgan's Laws: ~(PAQ) = (~P) V(~Q) Prove the tautology by using your program to construct the lexicographical possible truth values for p and q. Then create intermediate columns for binary operations such as ( P Q) and then ~(PAQ) " using the and, or, and not operators in python and your functions for implies and if and only if your created in program 2. End with the binomial operation of (left side of equation) if and only if (right side of equation). An example of what your output might look like is shown below. I--0-- --1--|--2--1--3--|--4--1--5--1--6--|--7--1 |--------I-PQ-IN(PQ) I-NP-|--NQ-NPVNQI-iff- - - - - - - - - - - - - - - - - - - True True True False False False False True ----- ----- ----- ----- ----- ----- ----- ----- True False False True False True True True - - - - - - - - - - - - - - - - - - - - - - - - - - - False True False True True False True True ! +------------------------- ----- -----+ ---+ False False False True True True True True >>>