Question

Write a C++ program to verify that the proposition P ∨￢(P ∧Q) is a tautology.

If you could include comments to explain the code that would be much appreciated! :)

Thank you so much!

Answer 1

#include <iostream>

using namespace std;

int main()
{
//boolean variable declaration
bool p,q;

//display table header
cout << "P Q P^Q ~P^Q (p v ~(P^Q)) \n";
  
//display the table data
for ( int i = 0 ; i < 4 ; i++ )
{
p = ( i >> 0 ) & 0x01;
q = ( i >> 1 ) & 0x01;

//display p and q
cout<<p<<" ";
cout<<q<<" ";

cout<<(p&&q)<<" "<<!(p&&q)<<" "<<(p||!(p&&q))<<endl;
}
return 0;
}

OUTPUT:

So, the given expression is a tautology because all output are 1 or true.