Question

Question 1 and 2 requires you to create a program ( you need to submit the source code and screenshot for the output), and question 3 and 4 requires solving the problems (no programs needed for those two questions).

1.Write a C++ program to construct the truth table of P ∨￢(Q ∧ R)

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

Answer 1

Question 1:

Answer:

#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:

Question 2:

A given boolean expression is a tautology if it is always true and doesn't depend upon the input.

The given boolean expression is:

P v ~(P^Q)

The above proposition is a tautology if the above proposition is true for all types of input values of P and Q.

The program source code to prove the tautology is given below:

#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:

The given proposition is a tautology because it result true always.