Provide the solution to these maths problems.

1.Four elements are in set A, 3elements in set B. How many elements are there in n(A X B)?

2.How many elements are there in A X A X A given that there are 3 elements in set A?

3.What becomes of the transfer function for a tachometer where a(t) equals the rotor displacement, e(t) equals output voltage and the tachometer constant is K.

4.What is thought of the unit delay operator given the z- domain?

5.How can you solve for the unit sample response given by 2(0.5)ⁿu(n).

6.What does counter integration, expansion into a series of terms and partial fraction expansion have in common?

7.Determine the probability through which sample K containing n items is selected without replacement from a population with N as the total number of items in sampling distribution.

8.Determine the value of bias in sampling for sampling distribution where E(X)=11 and =13.

9.Determine the type of function that is represented by a function that has the gcd of 'a' and 'n' as 1 whereas f(n) represents the number of elements present in the set {a: 0 <= a < n}

10. Justify the statement given that n is only prime given that n divides (2ⁿ- 2).