**PART I**

** Answer all questions**

**Question 1 (11* 2=22)**

1. What is a proposition? . [2]

2. State the two Absorption Laws of Boolean Algebra. Verify any one of them using the truth table.

3. What is truth table? [2]

4. State the principle of duality. Write the dual of:

(P+Q’).R.1=P.R+Q’.R [2]

5. State the DeMorgan’s Laws. Verify any one of them using truth table.

6. Using a truth table, verify if the following proposition is valid or invalid:

(A→B) ^ (B→C) = (A→C)

7. State the distributive law. Verify it using the truth table.

8. What is the canonical form of Boolean expression? State the two types of canonical form.

9. Find the compliment of: F(A,B,C,D)= [A + { ( B+C) . (B’+ D’)}] [1] [2] [2]

10. Reduce the following to its simplest form using laws of Boolean Algebra. At each step state the law used for simplification. {(CD)’+A} + A+ C.D + A.B

11. Verify that :-

(Z+X).(Z+X’+Y)= (Z+X). (Z+Y)

**Question 4 [5]**

The following function trial() perform are a part of some class. Answer the following parts given below. **Show dry run/working.**

int trial(int n)

{

if(n==1)

return 2;

else if(n==2)

return 3;

return trial(n-2)+trial(n-1);

}

void perform(int p)

{

int x;

for(int i=1;i<=p;i++)

{

x=trial(i);

System.out.print(x+” ”);

}

}

1. What will the function trial() return when the value of n is 4.

2. What will be the output of the function perform() when the value of p is 5?