Discrete Maths (DM) - Assignment No. 1

Discrete Maths (DM) - Assignment 1

Q. 1: Prove by mathematical induction 1 3 + 2 3 + …+ n 3 = [n 2 (n + 1) 2 ] / 4.

Q. 2: Use the laws of logic to show that the following proposition is tautology.

((p  q) ˄ ̴ q)  ̴ p)

Q. 3: Out of 250 candidates who failed in an examination, it was revealed that 128 failed in

mathematics, 87 in physics, 134 in mechanics, 31 failed in mathematics and physics,

54 failed in mechanics and mathematics, 30 failed mechanics and physics. Find how

many candidates failed

- In all three subjects

- In mathematics but not in physics

- In mechanics but not in maths

- In physics but not in mechanics nor in maths.

Draw a venn diagram.

Q. 4: Let m be a positive integer greater than 1. Show that the relation is an equivalence

relation. R = {(a,b) | a ≡ (b mod m).

Q. 5: Show that in a distributive lattice (A, ≤) if a ˄ x = a ˄ y and if a ˅ x = a ˅ y then x = y.

Q. 6: Determine the matrix of the partial order of divisibility on the set A. Draw Hasse

diagram of the poset. Indicate those which are chain.

A = {1, 2, 3, 5, 6, 10, 15, 30}

A = {3, 6, 12, 36, 72}

Solutions for DM assignment 1 is given below.