QUESTION SEVEN 

Find the co-factor matrix of matrix A below  (10)

Note: Indicate each number in the matrix by specifying its position - indicating its row and column and then calculate the value of the co-factor….The co-factor value should clearly indicate how you arrive at your answer.

QUESTION SIX

Use the Brute Force algorithm to solve the traveling salesperson problem for this graph by finding the total weight of all Hamilton circuits and determining a circuit with minimum total weight.  (10)

QUESTION FIVE 

Use Cramer’s rule to solve the following simultaneous equations (10)

5x + 3y = -11

2x + 4y = -10

QUESTION FOUR 

 Given U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

            A = {2, 4, 7, 8, 10} and    

            B = {3, 4, 6, 7, 9, 11}

4.1 Show that (A ꓵ B)’ = A’ ꓴ B’   (5)

4.2      Find (A ꓵ B) ꓴ (A’ ꓵ B´)  (5)

QUESTION THREE

 Given a =5, and d = 3 and a_n = 50, of an Arithmetic sequence. Find n and S_n. (10)

2.3 Find the determinant of the matrix below. (10)

2.2 Use a truth table to prove that the formula given below is a tautology or a contradiction. (𝑝 ∧ 𝑞) V (𝑝 → r)(10)

2.1 What is the output Y of the gate shown in the diagram below. Represent the output on a truth table. (10)

1.4 Given (5)

f(x) = 3x + 6   g(x) = 4x + k

and  f(g(x)) = g(f(x))

Find k.

1.3 Find the determinant of the matrix below(5)