MA4001NI Logic and Problem Solving Mock Test PDF

MA4001NI: Logic and Problem Solving Mock Test Paper: Week 7 1. Using truth table, show that [¬𝑝  (𝑝  𝑞)] → 𝑞 is a tautology. 2. Check the validity of the following argument. Robbery was the motive for the crime if and only if the victim had money in his pockets. But robbery or...

MA4001NI: Logic and Problem Solving Mock Test Paper: Week 7 1. Using truth table, show that [¬𝑝  (𝑝  𝑞)] → 𝑞 is a tautology. 2. Check the validity of the following argument. Robbery was the motive for the crime if and only if the victim had money in his pockets. But robbery or vengeance was the motive for the crime. Therefore, vengeance must have been the motive for the crime. 3. Using Boolean algebra laws, simplify the expression (𝐴 + 𝐵)(𝐴𝐶 + 𝐴𝐶̅ ) + 𝐴𝐵 + 𝐵 4. Given the logic circuit, a) Write the corresponding output function. b) Simplify the output function as much as possible. c) Construct logic circuit of the simplified expression. 5. Simplify (𝐴 ∪ 𝐵̅) ∩ [(𝐴 ∪ 𝐵) ∩ (𝐵 ∪ ∅)] as much as possible using the laws of sets. Also construct the Venn diagram of the expression so obtained. 6. Let U = {𝑥: 𝑥 ∈ 𝑁, 𝑥 ≤ 10} and A = {0, 1, 2, 3, 5, 8}, B = {𝑥: 𝑥 = 2𝑘, 𝑘 ∈ 𝑁, 𝑘 ≤ 3, 𝑥 ∈ 𝐵} and C = {the set of odd positive integers between 1 and 7 inclusive} are the subsets of U. Find: a) (A’ ⋃ C) ⋂ B b) List out the element of power set of B. c) Find the set D so that sets {B,C & D } forms partition on U. d) Does the sets {A, B, & C} forms partition on U? If not why, specify with reason.