Solution: DMTH137 Discrete Mathematics I Assignment 1 - S1 2019

This document provides a detailed solution to Assignment 1 for DMTH137 Discrete Mathematics I, covering a range of topics including logical connectives, truth tables, and graph theory. The solution begins with analyzing the "NOT OR" (↓) connective, constructing truth tables, and demonstrating how negation and AND can be expressed using only this connective. The assignment then delves into predicate logic, translating statements into symbolic form using quantifiers. Further, the document explores the truth values of propositions, including those involving quantifiers and predicates. It also presents proofs and counterexamples related to mathematical statements, examines set theory operations, and analyzes properties of relations, such as reflexivity, symmetry, and transitivity. The solution extends to graph theory, covering concepts such as graph completeness, Eulerian walks, Hamiltonian paths, and graph isomorphism. Finally, it includes a discussion on the validity of an inductive proof, addressing the scenarios of computer systems and their properties. The assignment solution is contributed by a student and is available on Desklib, a platform providing AI-based study tools.