Question

4. Rewrite the code below including the definitions of the function prototypes #include <iostream> #include <iomanip> #include <string> #include <stream> using namespace stod bool disjunction(bool.bool) bool negation(bool): bool implication(bool,bool bool equi bool,bool char btoc(bool value) return (value)?(T") ('F); string truthTable); int main( cout << truth Ta return 0; The functions conjunction), disjunction), negation), implication), and equivalence) should return the truth value of the conjunction, disjunction, negation, implication and equivalence connectives respectively. The functions truthTable) return a formatted string of a truth table that consists of all the connectives like the one on the formula sheet. Use the symbols &. I , !' > and = to represent conjunction, disjunction, negation, implication and equivalence in the tables respectively Extra Credit Prove or disprove that the wff is a valid argument by using a truth table, the Tautology Test and the derivation rules

c++
please include comments

Answer 1

// V stands for OR(disjunction),
//^ stands for AND(conjuction),
//' stand for NOT(negation),
//--> stands for NOT(A) OR B (implication)

//Evaluate expression
// (A V B) --> (B' --> A)
// !(A || B) || (B'' || A)
// !(A || B) || (A || B)

#include<iostream>
#include<iomanip>
#include<string>
#include<sstream>
using namespace std;

bool conjuction(bool a, bool b); // a && b
bool disjunction(bool a, bool b); // a || b
bool negation(bool a); // !a
bool implication(bool a, bool b); //!a || b
bool equivalence(bool a, bool b); // (!a || b) && (a || !b)

int main()
{
bool x[4] = {0,0,1,1};
bool y[4] = {0,1,0,1};
bool z[4];

// V stands for OR(disjunction),
//^ stands for AND(conjuction),
//' stand for NOT(negation),
//--> stands for NOT(A) OR B (implication)

//Evaluate expression
// (A V B) --> (B' --> A)
// !(A || B) || (B'' || A)
// !(A || B) || (A || B)

cout<<"Truth table\n";
cout<<"| A | B |Result|\n";
cout<<"-----------------------\n";
for(int i=0;i<4;i++)
{
z[i] = disjunction(x[i],y[i]); // (A || B)
z[i] = disjunction(negation(z[i]),z[i]); //!(A || B) || (A || B)
cout<<"| ";
if(x[i] == 0)
cout<<"False |";
else
cout<<"True |";

if(y[i] == 0)
cout<<"False |";
else
cout<<"True |";

if(z[i] == 0)
cout<<"False |";
else
cout<<"True |\n";

}

}

bool conjuction(bool a, bool b) // a && b
{
if(a==1 && b==1)
return 1;

return 0;
}
bool disjunction(bool a, bool b) // a || b
{
if(a==0 && b==0)
return 0;

return 1;
}
bool negation(bool a) // !a
{
if(a==1)
return 0;

return 1;
}
bool implication(bool a, bool b) //!a || b
{
if(a==1 && b==0)
return 0;

return 1;
}
bool equivalence(bool a, bool b) // (!a || b) && (a || !b)
{
if (a == b)
return 1;

return 0;
}

output:-

Truth table A B Result | False |False True | | False True True | | True False True I True True True /workspace/ $

Prove:-

All B !(A11B) CAILB CT) LT) (F)