Boolean Algebra Simplification (Exam Prep)

Question

I am preparing for an exam that I have on monday and the professor said that this would be on the exam for sure. I know the basic theorems of boolean algebra but I cannot quite simplify these 3. If someone could please explain how this would be done without using a truth table or k-map.

Answer 1

refer your notes. check out the identities you can apply to simplify these expressions. eg

1. Y=C(A+A'B')=>C(A+B') using(A+A'B)=A+B

2. Use De Morgan's law

3. if you solve first 2 you can do this one.

Here you can refer the basic rules.

Answer 2

Well using c++ and letting the computer do the hard work you could do it like this

# include <iostream>

 using namespace std;

 int main ()
 {
bool Y1,Y2,A,B,C;
Y1 = true;
Y2 = true;
B = false;
A = false;
C = false;

Y1 = A*C+(!A)*(!B)*(C);

Y2 = (!A)*(!B) + (!A)*(B)*(!C) + !(A+(!C));

if (Y1)
    cout << "First" << "True"<<endl;

if (Y2)
    cout << "Second" << "True"<<endl;

system("Pause");
return 0;

}