1.3 Find the determinant of the matrix below(5)

1.1 Prove that the proposition ¬(𝑝 → ¬𝑞) ≡ (𝑝 ∧ 𝑞 ) using equivalence laws.(5)

3.3 Use Cramer’s rule, solve the following simultaneous equations   (20)

3.2  If Universal Set U = {10, 20, 30, 40, 50, 60, 70, 80}

 A = {10, 30, 50, 70}                       B= {40, 50, 60, 70}

 C = {20, 40, 60}

a)     What is     (A ∩ B) ^c ∩C)

          b) What is         B ^c ∪ (A ∩C ^c)

            c) What is        A ^c ∪ (B ∩C) ^c                                                                                                                   (15)

3.1 The fourth term of an arithmetic sequence is 9.6 and the ninth term is

         15.6. Find the first term, fifth term and the sum of the first nine terms        (15)

2.3 Use a truth table to prove that the formula given below is a tautology or a contradiction.  (10)

(p ʌ q) → ¬p  

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

2.1 Prove that    𝑝 ∧ (𝑝 → 𝑞) ≡ (𝑝 ∧ 𝑞) using equivalence laws   (10)

1.3 Find the determinant of the matrix A below  (5)

1.4 If f(x) = x - 3 and g(x) = x² + 3x.  (5)

Calculate g(f(x))