Consider the following difficult questions and thoroughly work on them!

1.Given statement A X C B X C where A B, determine whether the statement is true or false.

2.Given that set B and A have 4 and 3 elements respectively, how many subsets are there in the set (A X B)?

3.Define the lagrangian.

4.Give three features of modern control systems.

5.1/(1-a) isn's system's step response. Solve for an LTI system the impulse response.

6.Define the difference equation and the conditions that result in the unit step response[1.099+1.088(0.9)ⁿ.cos(/3n5.2^o)]u(n)

7.In a club X, there are 30 players where 10 come from overseas. Determine the proportion of the population which is denoted by p.

8.Determine and justify whether there is truth in saying that k can be used to denote the variance of chi square distribution.

9.Given the base 2 (mod 19)for a number denoted as a which equals 7, determine the value of the discrete logarithm.

10. Solve for the value of 3²⁰¹mod 11.