Discuss the following.

1. Given the statement (A V B) ^ (C v D), what is its dual form?

2. Taking into consideration a square matrix of order n with a, b, c as Eigen values, determine the Eigen values of matrix AT.

3. Find the value of S where the inequality 49x2 - 4a4 0 is the solution of the inequality log1/2 x2 log1/2 (x + 2). Parameter a has a set of real values which are denoted by S.

4. What is denoted by a random variable X given that the expectation of the variance is denoted by E.

5. In XTS-AES mode, a tweak is used to provide a different output for the same input PT and same key. True and false?

6. Determine the truth value of the fact that the hard knapsack becomes the private key in the Merkle- Hellman Cryptosystem while the easy knapsack becomes the public key.

7. Which system is the Public Available directory more secure than given to choose either between Public key authority and public announcements? Explain

8. Determine the no. of states that are needed to make a password-pass system using DFA given that administrator is the password to the admins.

9. Suppose equation x2 + 3x + 3 = 0 and x2 + bx + c = 0 have one root in common, find sum of b + c.

10. How many squares are there in a 8 x 8 chess board?